{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 20)\n",
"options(repr.plot.height = 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## Revisiting Time Series Decomposition and (S)ARMA models\n",
"\n",
"We will revisit some of the examples for Time Series Decomposition and Seasonal ARMA model estimation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
airpass {fma} | R Documentation |
\n",
"\n",
"Monthly Airline Passenger Numbers 1949-1960
\n",
"\n",
"Description
\n",
"\n",
"The classic Box & Jenkins airline data. Monthly totals of international airline passengers (1949–1960).
\n",
"\n",
"\n",
"Usage
\n",
"\n",
"airpass
\n",
"\n",
"\n",
"Format
\n",
"\n",
"A monthly time series, in thousands.\n",
"
\n",
"\n",
"\n",
"Source
\n",
"\n",
"Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley\n",
"& Sons: New York. Exercise 2.4, Chapter 3, Exercise 4.7.
\n",
"\n",
"\n",
"References
\n",
"\n",
"Box, Jenkins and Reinsell (1994) Time series\n",
"analysis: forecasting and control, 3rd edition, Holden-Day: San\n",
"Francisco. Series G.
\n",
"\n",
"\n",
"Examples
\n",
"\n",
"plot(airpass)\n",
"seasonplot(airpass)\n",
"tsdisplay(airpass)\n",
"
\n",
"\n",
"
[Package fma version 2.3 ]
"
],
"text/latex": [
"\\inputencoding{utf8}\n",
"\\HeaderA{airpass}{Monthly Airline Passenger Numbers 1949-1960}{airpass}\n",
"\\keyword{datasets}{airpass}\n",
"%\n",
"\\begin{Description}\\relax\n",
"The classic Box \\& Jenkins airline data. Monthly totals of international airline passengers (1949--1960).\n",
"\\end{Description}\n",
"%\n",
"\\begin{Usage}\n",
"\\begin{verbatim}\n",
"airpass\n",
"\\end{verbatim}\n",
"\\end{Usage}\n",
"%\n",
"\\begin{Format}\n",
"A monthly time series, in thousands.\n",
"\\end{Format}\n",
"%\n",
"\\begin{Source}\\relax\n",
"Makridakis, Wheelwright and Hyndman (1998) \\emph{Forecasting: methods and applications}, John Wiley\n",
"\\& Sons: New York. Exercise 2.4, Chapter 3, Exercise 4.7.\n",
"\\end{Source}\n",
"%\n",
"\\begin{References}\\relax\n",
"Box, Jenkins and Reinsell (1994) \\emph{Time series\n",
"analysis: forecasting and control}, 3rd edition, Holden-Day: San\n",
"Francisco. Series G.\n",
"\\end{References}\n",
"%\n",
"\\begin{Examples}\n",
"\\begin{ExampleCode}\n",
"plot(airpass)\n",
"seasonplot(airpass)\n",
"tsdisplay(airpass)\n",
"\\end{ExampleCode}\n",
"\\end{Examples}"
],
"text/plain": [
"airpass package:fma R Documentation\n",
"\n",
"_\bM_\bo_\bn_\bt_\bh_\bl_\by _\bA_\bi_\br_\bl_\bi_\bn_\be _\bP_\ba_\bs_\bs_\be_\bn_\bg_\be_\br _\bN_\bu_\bm_\bb_\be_\br_\bs _\b1_\b9_\b4_\b9-_\b1_\b9_\b6_\b0\n",
"\n",
"_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n",
"\n",
" The classic Box & Jenkins airline data. Monthly totals of\n",
" international airline passengers (1949-1960).\n",
"\n",
"_\bU_\bs_\ba_\bg_\be:\n",
"\n",
" airpass\n",
" \n",
"_\bF_\bo_\br_\bm_\ba_\bt:\n",
"\n",
" A monthly time series, in thousands.\n",
"\n",
"_\bS_\bo_\bu_\br_\bc_\be:\n",
"\n",
" Makridakis, Wheelwright and Hyndman (1998) _Forecasting: methods\n",
" and applications_, John Wiley & Sons: New York. Exercise 2.4,\n",
" Chapter 3, Exercise 4.7.\n",
"\n",
"_\bR_\be_\bf_\be_\br_\be_\bn_\bc_\be_\bs:\n",
"\n",
" Box, Jenkins and Reinsell (1994) _Time series analysis:\n",
" forecasting and control_, 3rd edition, Holden-Day: San Francisco.\n",
" Series G.\n",
"\n",
"_\bE_\bx_\ba_\bm_\bp_\bl_\be_\bs:\n",
"\n",
" plot(airpass)\n",
" seasonplot(airpass)\n",
" tsdisplay(airpass)\n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"?fma::airpass"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"airpass <- fma::airpass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can examine the data plot:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAMFBMVEUAAABNTU1oaGh8fHyM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\n/QfXVL6lhxAq+AAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(airpass)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"\n",
"Note the totak number of years in the series:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 12\n"
]
}
],
"source": [
"total_years <- length(unique(floor(time(airpass))))\n",
"print(total_years)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also plot the seasonal plot:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAC/VBMVEUAAAAAAP8AaP8AjP8A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",
"text/plain": [
"Plot with title \"Seasonal plot: airpass\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::seasonplot(airpass, year.labels = TRUE, year.labels.left = TRUE, col = 1:total_years)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the $\\rm ACF$ and $\\rm PACF$ plots:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nBwoR2TsjWwAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(airpass)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and note the ACF slowly declining and the decline is in waves, which appear to repeat every `12` lags - this indicates seasonality. The time series chart indicates that there is an increasing trend."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Time Series Transformation\n",
"\n",
"The variation appears to be increasing, which also indicates that the series may be multiplicative: $Y_t = T_t \\cdot S_t \\cdot E_t$.\n",
"\n",
"We want to take logarithms of the data, to get an additive form: $\\log(Y_t) = \\widetilde{Y}_t$ so that $\\widetilde{Y}_t = \\widetilde{T}_t + \\widetilde{S}_t + \\widetilde{E}_t$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"log_passengers = log(airpass)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\n9wAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(log_passengers)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now the series appears to be additive. We can move on to decomposition of the series."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Decomposition via Moving-average\n",
"\n",
"### Trend Decomposition\n",
"\n",
"We can decompose the series manually via the `filter(...)` function:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"one_sided_trd <- filter(log_passengers, filter = c(1/24, rep(1/12, total_years - 1), 1/24), sides = 1)\n",
"two_sided_trd <- filter(log_passengers, filter = c(1/24, rep(1/12, total_years - 1), 1/24), sides = 2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nAgCITMACAIhMwAIAiEzAAgCI7H8jEW90oE4BHQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"Log of Airpassangers\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(log_passengers, main = \"Log of Airpassangers\")\n",
"lines(one_sided_trd, col = \"red\")\n",
"lines(two_sided_trd, col = \"blue\")\n",
"legend(x = \"topleft\", legend = c(\"Actual\", \"One-sided MA Trend\", \"Two-sided MA Trend\"), lty = 1, col = c(\"black\", \"red\", \"blue\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Seasonal Decomposition using the decomposed trend\n",
"\n",
"Next, we move to decompose the seasonality"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"#seasonal component of one-sided averaging\n",
"one_sided_season <- log_passengers - one_sided_trd\n",
"one_sided_season <- matrix(one_sided_season, ncol = 12, byrow = TRUE)\n",
"one_sided_season <- apply(one_sided_season, 2, mean, na.rm = TRUE)\n",
"#seasonal component of two-sided averaging\n",
"two_sided_season <- log_passengers - two_sided_trd\n",
"two_sided_season <- matrix(two_sided_season, ncol = 12, byrow = TRUE)\n",
"two_sided_season <- apply(two_sided_season, 2, mean, na.rm = TRUE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We then scale the seasons to sum up to 0:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"one_sided_season <- one_sided_season - sum(one_sided_season) / length(one_sided_season)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"two_sided_season <- two_sided_season - sum(two_sided_season) / length(two_sided_season)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAMFBMVEUAAABNTU1oaGh8fHyM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\n7l+A+OXeAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title \"Seasonality from Two-sided trend decomposition\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"plot.ts(one_sided_season, main = \"Seasonality from One-sided trend decomposition\")\n",
"plot.ts(two_sided_season, main = \"Seasonality from Two-sided trend decomposition\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using $S_t = S_{t+d}$, create the series for the full years:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"one_sided_season <- rep(one_sided_season, times = total_years)\n",
"one_sided_season <- ts(one_sided_season, start = start(log_passengers), freq = frequency(log_passengers))\n",
"#\n",
"two_sided_season <- rep(two_sided_season, times = total_years)\n",
"two_sided_season <- ts(two_sided_season, start = start(log_passengers), freq = frequency(log_passengers))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we can examine the decomposition visually"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nwiBYAAAAAMIgWAAAAADCIFgAAAAAwvwPeMAJxjSPIEkAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title \"Two-sided averaging decomposition\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"#\n",
"plot(log_passengers, lwd = 2, main = \"One-sided averaging decomposition\")\n",
"lines(one_sided_trd, col = \"blue\", lwd = 2)\n",
"lines(one_sided_trd + one_sided_season, col = \"red\", lwd = 2)\n",
"#\n",
"plot(log_passengers, lwd = 2, main = \"Two-sided averaging decomposition\")\n",
"lines(two_sided_trd, col = \"blue\", lwd = 2)\n",
"lines(two_sided_trd + two_sided_season, col = \"red\", lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also use the `decompose(...)` function to do all of this:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"two_sided_decomp <- decompose(log_passengers, type = \"additive\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compared with the `filter()` function:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec\n",
"1949 NA NA NA NA NA NA 0 0 0 0 0 0\n",
"1950 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1951 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1952 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1953 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1954 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1955 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1956 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1957 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1958 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1959 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1960 0 0 0 0 0 0 NA NA NA NA NA NA"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"two_sided_trd - two_sided_decomp$trend"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results are the same. The upside is we automatically get the seasonal decomposition as well, which are the same as our manually calculated ones:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec\n",
"1949 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1950 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1951 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1952 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1953 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1954 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1955 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1956 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1957 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1958 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1959 0 0 0 0 0 0 0 0 0 0 0 0\n",
"1960 0 0 0 0 0 0 0 0 0 0 0 0"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"two_sided_season - two_sided_decomp$seasonal"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also plot the series:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nAACRCSwAgMgEFgBAZAILACCy/wEEgfkZeUMxRwAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"Log of Airpassangers\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(log_passengers, main = \"Log of Airpassangers\")\n",
"lines(two_sided_decomp$trend, col = \"blue\", lwd = 2)\n",
"lines(two_sided_decomp$trend + two_sided_decomp$seasonal, col = \"red\", lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and examine the residuals:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(two_sided_decomp$random)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the $\\rm ACF$, the residuals still appear to have some searonality."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"## Exponential Smoothing examples\n",
"\n",
"### Simple exponential smoothing:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"s_es <- forecast::ses(log_passengers)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAPFBMVEUAAAAAAP9NTU1oaGh8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\nAACgMAIWAABAYQQsAACAwghYAAAAhf0fkFxFyRVkbOwAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title \"Forecasts from Simple exponential smoothing\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"#\n",
"plot.ts(log_passengers)#, main = \"Simple Exponential smoothing\")\n",
"lines(fitted.values(s_es), col = \"blue\", lty = 2, lwd = 2)\n",
"lines(fitted.values(forecast::ses(log_passengers, alpha = 0.1)), col = \"darkorange\", lty = 2, lwd = 2)\n",
"#\n",
"plot(forecast::forecast(s_es, h = 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Double Exponential Smoothing (Holt's Linear Method)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"d_es <- forecast::holt(log_passengers)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAPFBMVEUAAAAAAP9NTU1oaGh8\nfHyMjIyampqnp6extc6ysrK9vb3Hx8fQ0NDZ2dnb29/h4eHp6enw8PD/jAD///9W3QYnAAAA\nCXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO3diXqqSBCG4Y7GONlOYrj/ex1BUZbeu4AC\nvveZOXGB7lKx8wdaNBUAAABEmaULAAAA2BoCFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAA\ngDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAA\ngDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAA\ngDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAA\ngDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgAAgDACFgBg\nTqZDvPE3913vB2M8d/s8K7XX/Lj1zb1MtDdPR+7CoA4vDQBgThMGrO+Du8X3ur9pA9a9+6LH\n1T4EAtbq8dIAAOY0YcDytXg05qe8XW/A6v8o64qAtXq8NACAOU0YCnxNl3SbFrCO5pDdEwFr\nO3hpAABzGoWCr7f64N3X497fozlfL13OB3M4/95uvpyPxrzel/k8XZc63u66vL9er5w+q8eu\nsf6No26fHYw6rj6O5vhdVR8H8/ptL/lxabTus/uTOQ0q6zU07uT5SJ8Pof73+9rA26/tWap+\n3w7m+EHA0oyXBgAwp2EoeL2nilN7bx2lrhHicLu5CSHtlXN3hfqu9o56jUc66d747PSZXG4d\njDu+3fB7fvY7Krm9NFq308V7U6alCEcnnUfaK/O2yOHX0uH3vWkClmK8NACAOQ1CwamNS7fs\ncLv4WVVtPmkOt7VXzFdVfVyDxaWqzs0Kb82yl2vS+Himk+6Nz06fyeXWgbXjusNukhmWfL80\nXrfbRcNShKOTziMdlll7s3R4eN4t8ZJgCrw0AIA5mV44+Lr++LhUl/dbemr28Vzj0z1GXW4x\n5Xrl8NOElWMzW/333s7tgN/18qW5pzMXqnPjs9v2Z9OBveNrT+b40/ywl+wquttFu461iFEn\nvUfaLfPw3cTIw7jDz+ut1x9fBwKWYrw0AIA59bPKW7uH53zbV3OPLPUum8tt6VNzpb7xcnz/\n7bVz25XzmJjUppP+jf37Hh1YOv7u/bCX7Cq6Gq7kKmLUSe+RDsu8WDu8Px9N7vI801gULw0A\nYE79rGLu8aL67V9/LnQYT9v6/Ty/3tZ/vy1zTzL35fo3Prttf166PzsdV6Mf45JdRY9W8hXR\n+9F7pKNPEVo7fHREwFKMlwYAMKdRduld6gSLZ6Lpr/J57GSdcxtOfjsr924cdDT8OejYFbCs\nRdrXvfMU4QhYg8fv7pCAtQa8NACAOY2yy2PfTHcPzmEwn+l55fN67fj28XO/8fJ5+4Dda3e5\n7o2DNoZ7sgYdxwYsz7otdxG9HwdrV+49WAcC1jrw0gAA5tQPBSf7dKbHNKPGa3cO1vF+T6ed\n5hxRw6bbGwfddjrwzKPyByz/ul32Ino/eo/UEbBO9jlYnwQsxXhpAABz6ocCxwfymg/KfTc/\nXgefIrwvcduDdXzMqGr3JF2GNw66bX/6PwnoD1iedS/tOr4iej96j/TRRr/cQYcft08RfvIp\nQs14aQAAcxqEgsdpQ28nfHrc+zjV03f3ykezwvlxioJr8nj9bWaUn++LnYc3Drp9dGDvOCpg\nOda9d3/jK6L/Y/RIz+NyBx1yHqwV4KUBAMxpGApeu8nhee/X/eYmnnx3zuR+P4t5fa7O7+dU\n8mai09v9Qu/GQbfP7q0dxwUs+7pvvS49RfR/9B5p28aw3H6H9+fgRMBSjJcGADCnUSj4ejsM\nvtav0Xz94OmrvXJ4XPm5hpDD28/v7cRRzSyn1/vZ0k/3BNK7sd9wp3tbx5EBy1502327iKuI\nQSe9R3rqz0Wzd1j9vjVNE7AU46UBAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQ\nRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQ\nRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQRsACAAAQ\nRsACAAAQRsACAAAQRsACAAAQVhiwPo7GnL5kSgEAANiG3IBlmhVfTeMsWBAAAMDaFQWsszlf\nqur3bD4kSwIAAFi3ooB1MJf68sUc5QoCAABYu6KAZUznCgAAABpFAeutDVgHqXIAAADWLz9g\nnd4/vszn9eLlzCx3AACAp/yAddNcPFwkSwIAAFi37NlTPz8fH6dTM9X9TL4CAAB4Yno6AACA\nMAIWAACAMAIWAACAMJGA5T8PlgEAC4nRR9rSzwkAnTJGE5khyTtISXQBYGtUDg0qiwKwtKUC\n1uJdAFgflUODyqIALI2ABWA1VA4NKosCsDQCFoDVUDk0qCwKwNLmDFiXc/0FhO9HY14/J+oC\nwJapHBpUFgVgaTMGrN+DMdXlcJvF/jpJFwA2TeXQoLIoAEubMWC9mdPl+s/b7zVrvfm/7JkB\nC4CFyqFBZVEAljZjwDLmcv+nqi7mMEUXADZN5dCgsigAS5s1YF3/OZjOFfEuAGyayqFBZVEA\nljbrIcKfqnqv/6n3YHknYTFgAbBQOTSoLArA0mYMWD/mcP6pTodrwvo6mq8pugCwaSqHBpVF\nAVjanKdp+Do8vwvnfZouAGyZyqFBZVEAljbviUY/3451ujq9/07WBYDtUjk0qCwKwNI4kzuA\n1VA5NKgsCsDSCFgA5vHy8lLahMqhQWVRAJZGwAIwj5fyhKVyaFBZFIClEbAAzOOlPGGpHBpU\nFgVgaQQsAFO7vaOv6YqABWAvCFgAptZ8c0P5DCylQ4PKogAsjYAFYGpG6j2tcmhQWRSAqfyL\nXI6ABWBippJ6U6scGlQWBWAqBCwASpjHPyItaaOyKAAT+UfAAqCE6fwr0ZIyKosCMI1/BCwA\nWpjeD4GWdFFZFIBpELAAqGF6P0s+TahyaFBZFIBJ/CNgAVCjH7BKEpbKoUFlUQAmQcACoMZj\nxxUBC8C6/SNgAVCDgAVgG/4RsADo8Zx6VTwJS+XQoLIoABMgYAFQZBiwChKWyqFBZVEA5P0j\nYAFQpHk/N6GKgAVgvf4RsAAo0jkuSMACsF4ELACaELAAbME/AhYATcYBq7QtZVQWBUDYPwIW\nAFWeU7DK39oqhwaVRQEQRsACoItxXC5tSw2VRQGQ9Y+ABUAXAhaA1ftHwAKgi3FeKW1MC5VF\nAZD0j4AFQBkCFoDVI2AB0IaABWDt/hGwAGhjC1jZJ8JSOTSoLAqAIAIWAHWM7VpuwlI5NKgs\nCoCcfwQsAMJe8s+6ftc9DRYBC8AKEbAASHspTVid87g/rxKwAKzHPwIWAHkErBCVRQEQQ8AC\nIKn4m5k7rRCwAKzVMF8RsAAUMIaAFUllUQCkELAAyDHswYqmsigAQkb5ioAFIJuphALWqJFB\n4MprTheVRQGQMc5XBCwAmZqjgy8vEu9DR8AqbE4XlUUBkEHAAiCl3ckkF7A6O6wIWABWxJKv\nCFgA8sgHLN8NZc1poLIoACIIWADEELDSqCwKgARbviJgAcjTfrkNASuOyqIASCBgARDzmDYl\n8D60NNG96e+v+yOvveWpLAqAAGu+ImAByLJEwIqNWCqHBpVFARBAwAIg5/nBv7JzVj3bcjT/\n3HNFwAKgkD1fEbAAZGmnYEmcatS9B+vaaHSs8ra3PJVFAShHwAIgyAwvlQas/vrdgJXXnjYq\niwJQzJGvCFgAsggGLNsxxkejGflK59CgsigApVz5ioAFIIcZXZwmYGUcIFQ6NKgsCkApAhYA\nSVMHrLbVnHylc2hQWRSAQs58RcACkEM8YA1XL2lV5dCgsigAhQhYAESZ0WUClp/KogCUcecr\nAhaAHASsVCqLAlCGgAVAVjcUjd6JaROn7Pms5O2tcmhQWRSAIp58RcACkMMXsBI/+WfdgUXA\nAqCeL18RsABk6O11GrwTU8+s4HgjF7y/VQ4NKosCUIKABUCYP2DltGW5OesUDZ4Wl6WyKAAF\nvPnqv8hGCFgAOnqH9frvxGcsigxIBCwAq+TNVwQsABn686a6b8W/bsCKSUiu9zEBC4Bq/nxF\nwAL2xZR8KXO3mcoZsLqXIyKSM2Bl5yudQ4PKogBkC+QrAhawK8a8XGNRecayBSxLq38REcv5\nPr6tmlOryqFBZVEAsgXyFQEL2BNTmSawlCaswZkV3CcFjUhYgYCVU6vKoUFlUQCyBfIVAQvY\nEdPGFZGANbpqbTWYsOynwXoeayRgAVAolK8IWMB+NPlq7oAVTFgELAArFMpXBCxgP5qA5coz\nqS1Zrjpa9Qcs1/yt61rZ33GocmhQWRSATMF8RcACdqN+w0wTsEq+7tmzavb3PascGlQWBSBT\nMF8RsIC9uOUr5xG55LbG17POq+Cph4AFQKlwviJgATthuj/XEbCyd4zNPjR8HI05ffmXYbwC\nNiScrwhYwE5IBqzRW2+3Acs0Xb2axtm/6CwFAZhDRL4iYAE7YQY/i9vq5p7mhvx85Q9YuY3O\noQlYZ3O+VNXv2Xx4F52pJADTI2ABuDOjC6WNCQYs1z6qlQSsg7nUly/m6F10loIAzCAmXxGw\ngH1QHbDG7m1lFjtzwDKmc8W96AzlAJhFTL4iYAH7MG3Aqm8J5Sv7/VsIWG9twDp4F52hHABz\niMpXBCxgHwhYkzDm9P7xZT6vFy9n/yx3xitgKwhYAFqdueTl7xvLvCkTcYDQuoS9mnbRFQSs\nm+bi4eJddKaSAEwtKl8RsIBdmD5ghdkCln8HVm6xMw4NPz8fH6dTM9X97M1XjFfAVsTlKwIW\noNnLXXFDw4BV1KQ7YPmbtSSsuICVWq3KoUFlUQDSxeUrAhag2MtkAasoYZnx+vkBy7bKc8Go\ndq0FqqOyKADJIndgEbAAxQSS1V1np5NMwLLfFGh1lLDqfOUNWHnVqhwaVBYFIFlkviJgAYr5\nT6yU0lDz74QBK67VYcAK56tVBSzOgwXsQGy+ImABSjWfTVMZsKxFZRzLM458ZWl3rQHLdC1R\nEgBpsfmKgAWodP91vOWAZZnJJdJupXRoUFkUgFQELGDVzOCnRHP3kDJFwPr7Sw5CsR9mzClX\n5dCgsigAiaLzFQEL0Ej0vOuDVnQErOgqCFgAFInOVwQsQKNBwCr9NKEZX8tv0va+ywxYMUsr\nD1iXc/0FhO9HY14//UsyXgEbEJ+vCFiARsM9WIUJyxKwChsbFPT3l9hq/NI51c43NPwejKku\nh9ss9lfvooxXwAYQsIB1e0wAX0fAqs+rENvq7RwMWwlYb+Z0uf7z9nvNWm982TOwdQn5ioAF\nKPTMMCIBy3ivZrU2YcAanywr2XxDgzGX+z9VdTEH76LzVARgQgn5ioAFKCR63nXhgGUrKCVg\n3QLUdgLW9Z+D6VxxLzpDOQCmlZCvCFiAQqOAJfDlzM6rOY2Np2ClBayEfKV09Ll7Mz9V9V7/\nU+/B8k7CYrwCVi9lBxYBC9BnfNYqgYD1bEE8YCVOq/LPiF9XwPoxh/NPdTpcE9bX0Xz5FmW8\nAlYvJV8RsAB91hawEpv1BqxRvlI6+rS+Ds/vwnn3Lsl4BaxdUr4iYAH6CAes4aypomld7pXj\nK72FKPuCroCVVO6sQ8Pn27FOV6f3X/9yjFfA2iXlKwIWoE9vJ1H5Zj5KKCUJy32C0LbQcLue\ngDXOVzkRU+XQoLIoAAmS8hUBC1Cnn2E0BizvXbFffxMbsDLKVTk0qCwK2LPUN2XaDiwCFqCO\n6GlBK0ucWTpgufu35SsCFoBJ+M+sMpaWrwhYgDrCAWucT1QErPjuCVgApmDS3paJ+YqABaij\nOWD5qiFgeaksCtix+j2ZshOLgAWsnOhpQavpA9bjsB4By0tlUcCOmc6/MRLzFQEL0Ga4XZdu\n5+P1JwpYse2mdk/AAjAB0/sRlJqvCFiANvaAlX8iLJ0B68U6n93TZ/e7r+PWUEZlUcCOEbCW\n7QKY22iz7h95i88lzgYL3jm2CDUMWJGN/KUmrOQelFFZFLBfZvAzIDlfEbAAZRwnVcgOWJa3\niWjA6hQU1267VHzCMqMLsStoorIoYL8KAlZUviJgAcr4A9YjlKSnk8BtCY3JBKxRwnI+JAIW\nAHFpA0v6DiyVAev7/dR8c+rp/D1VF4Ba44/YdVLNXydgRSasiIAVv1PM8vm/bh1Rb8nnQoPH\nQMACMJ/8gBWXrxQGrMvx+eX05nWSLgC9LPuInruwuokkNmGFA9ZfYlgTC1j9x+CugoAFQNwO\nA9bZHD5/mku/XwdznqILQK9AwOrcHBmLbCed6r11/v6iE5b/CGHcW3LQd7eK0CrR73iVQ4PK\nooDdSvzwTHq+UhiwDubncfnHHKboAtDLF7BGc5ZiYlFEwIreiWVry9luX+DLq70FELAASEsL\nWBk7sBQGrN556/0nsWfAgiov+eeqekoIWHEJyx2wujfKBCz3mbBeegFrtIC/+/7nKCOoHBpU\nFgXsVnbAis1XCgMWe7CwVi8vAhHLFlGcW3pEKrJGnuTE0lnNu5K1YTPMV6M2QvEutV6VQ4PK\nooDdMtaLLtsIWGdz+PptLjEHC+siEbB8eUi8wayAFbNEfwec6e7bcwSsmGYNAQuAEOO4bJeT\nrxQGrOq18ynC42WSLgBZziNjmS3F3JjUoEjAiijD0nBv/1XETjB3swQsAFL2GbCq73NzHqzD\n6Z3zYGEdjLHOLMppKfrGpAaXC1jdfHX9ScACoEFuwIrPVyoDlqYugBim/k8iX80UsDy73MIn\nS/AuPUxYt+DZrnq/lBewEp5hlUODyqKAvcoMWAn5ioAFlDOPf2SairoxpcFRMrm1aAtTEaf7\n7C1tX6jt0PRXvd2cnkQJWABEGecVm6wdWAQsoNz9CJbEBmlvw2R8ybOvPU/AciYsa7oJBCwz\nuPl2OwELwMKM59pYVr7SHrA4DxbWwPR/FhwrdOeha5RxtevLXr6A9fdnbfBv9OU391g0Xnrc\nc+8pMMObm1lUOU+PqQhYAB6K304ELEvAMl0SXQDFBgGrIGF5A5ar3ZiToNtudq3WC1jt7H1j\nOwuFM2ANr3QDVg6TNqKoHBpUFgWskcCv/6SAlZevtAesxbsAwuwHwgqaskyZaqJMxi4sT8By\nr9W5x9w+Bth+GjB8/irHzNH7UdTcp4aABeDOJI4H9kY810by8hUBCyg22lEzd8BK/OhfFQ5Y\nf50FjXGdXsHWwihUdS6b7KeGgAWgYUQ+VGS8V4cIWMBCpg9YlQkFrJSP/t1u983cetz3qMfa\nTkzA6n6ekIAFoMxwQkZhM3Gt5eUrjQHrcq6/gPD9aMzr50RdAJLaaUoTBqx7lEnfhZUXsEb1\nROerUMDKZNLWVTk0qCwKWJlpApa/ucx8pTBg/R6MqS6H2yz210m6ACR1ckRpwHLlq2DAcsUl\nZ4Mm7rQP3oDlW+VxqXPK0YI3LAELQI2AlblK482cLtd/3n6vWeuNL3uGfjMErDYNCQassoKC\nqzwuyQSsxJOMqRwaVBYFrMvoI0WFzUQ1l5mvFAYsYy73f6rqYg5TdAFI6uaIjEAyasqThzK/\nxM+2Wlyl1rntkV0O1y16vxKwACwTsHLzlcqAdf3nYDpXxLsAJD2nYAntts7f4RTfYGRky3/n\nj792sCxgTbj0TFQWBawLASt3lcab+amq9/qfeg+WdxIWAxY0kA5Y1syT2XBhwMrqtTdvS+Qb\nsJMrUTk0qCwKWBcCVu4qjR9zOP9Up8M1YX0dzdcUXQCCRp+VK20r8Z6IBjMD1t+fnoCVU4Iy\nKosC1sVYLhU1E9Fcbr5SGLCqr8Pzu3Dep+kCkBMIWClf0uzZosUDVsQkLN9X8ET02d2zNzOV\nQ4PKooBVMdaLJc1ENLelgFVVn2/HOl2d3n8n6wKQ0s8Rw40yKaSIByzfbqqoXVg595V+lFKA\nyqFBZVHAqiwWsHLylc6ApagLIMR4rv2l7QSaKGDZT/sQk4M81ROwUqksClgVAlb2Kgq7AAKM\n52pivnJs0bc2wlt74JuXh4vGBSxX/b4HFj74ODWVQ4PKooBVIWBlr6KwCyDAHrCadJE8hykc\nsBL3NxUGLNM8BOsSBKxkKosCVkUmYNlW9QesrHxFwALKOPZg1fEieY54xB6stClTvoAV8f4x\nzZK2Lr0Pzfi6noXKoUFlUcCqGMfl/FYimiNgAcsYboUlM5DsJzaIDljj2ON4i8QedHTviiJg\npVNZFLAmxnklv5lwc7n5ioAFFBlthAUBy55n7lkmJ2B5d2CVBKzAvjkT1fqEVA4NKosC1oSA\nlb+Kwi4Av+iAFXG8sDhgDTsRDFj9+WSRAWuxaVgqhwaVRQFrQsDKX0VhF4Df6KhedxJWV8SM\nd2/Aipo6nhSwwm+gfsCKn1JGwLJRWRSwJjIBy76iJ2Bl5isCFlBkPG3KvQsrFFCmCVj2s2B1\nKg3U0zbwF5+xjLPrmagcGlQWBcxG4B0wZcByt0fAAhYRH7DCCcsaoR4rZZz8IJBy0gJWymm9\nDAFrTGVRwFxM+TvAeK5lNxNuLzdfEbCAEpbU09z092edGh6euuROJZMFLOcCGT0+1rwdISRg\ndagsCpiHMQLvAOO9mttMsDkCFpBK4te/JcLcA5ZtaX/CCuSd3Deh52HK9/hYk4A1orIoYBYy\nnyyWCVjO1Vx3ELCAVBK//9MCVsTpo0L7k1Lci1swYGU3UEjl0KCyKGAOpvNvcTOuq5mthO8g\nYAGpJgpY9W3J53B/tFVwv30F/1fhVL5FCt5gC783VQ4NKosCZmB6P4rbcVzNbCV8BwELiNfu\nK9pBwPI+Rk/Aqp8cApYolUUBMxAKWMP1pQOW6x4CFhDPiH3GzZZhlgxYvb7Dh+ncCesasEre\nXwSsMZVFATPYZcB6if4TnoCFLTFSM4Ssm6DJy1cyAatNWM4dUL3afMcIl5tBVU7l0KCyKGB6\nZvCztB3X9bxWwndlpisCFvbIiG07voCVGlCsbXXj0FwBKzAzaw1UDg0qiwKmN1XAymvQt5L9\nvsx4xSFC7NHEAavNMIkJJRiwwpPWb4/sxZvvogPW7dZ1xiyVQ4PKooDpmdGFwnaK2ps6YLXp\n6j8CFvbIVFIbj72V0C4gyxHE2w6nwDdEt3PzvfU0AevPPYXfFrAGbXTrJ2CJUVkUML09BaxO\nvCJgYY+WD1jdLwO855gXYzlknxGwqms719WMazlbk4M22hmpdQsELDEqiwImZyyXytopac+/\njvXevHRFwMIumcc/pQEiL2A9v23ZPHZb2adE5gSseoG/P9v+sHGLjiHr/gQRsESpLAqY3E4C\n1sswXhGwsEP9jwyXJAjHFhhu+R5zTBtjrlHLdkjPmobiApZrwZSAFepNL5VDg8qigMntImCN\n0xUBC3skHLAsDQSzyTNg3Q7EOTbl1ID1WMD91ogKWLfMF+pNMZVDg8qigMlNF7AyGgytYbs/\nMl6NbxaqSWYVhV1gg9rkUJ6wsgPWLecE89BwNnyo3Xs9nq+tt7c4biKiM81UDg0qiwLcjDEC\nW62xXixqJ7vB8OPJCViOeEXAwg6pC1ix+SouYFUp7wxXwDIELHEqiwIcbuFKNmAVNScQsCIW\nTw1YlplXBCzs2GDHkXDAqlNReMvs78FK6i8iYCUYNNk+IuNOj2ugcmhQWRTgYDr/CjQ0vlzS\nTl57UUtbFgqlK0e8ImBhhzQErH4hSf0V3O9epS3i8YgkDg0sR2XxKosC7NJ3h4daKm2tOGDF\nLRwfsPzhioCFPXrGmtKAZV0/NWCldO9s96UzaypNP2B1nptVv7tUFq+yKMBOXcCyrrpgwAqm\nKwIWdqgTiwqPgjkDVv47OWeNxym0hALW7fKq310qi1dZFGAnFrCM80pBOzkNJh1Y6MmMVwQs\n7M8wYIm09HCbmJ57rD9jlc4ZSvv3Wr6Qx90iAWt6KosCrMzoQnFLha3NFbAsy1nTVTheEbCw\nP8IBy7YDa+aA5bg3PWGteV57j8qhQWVRgBUBq8OSrmLiFQEL+yO3l8a2+swBq3uemmE8+hsk\nLHvgGgWsLVD5QFQWBVgZy6XSlopac6wY3170kt6AlZCuCFjYH6mPtDhW7wUs/84g/x4m672D\nHvsnqhntfxokrGDA2s4bSuUjUVkUYGOsFwtbKmrNtWJBbopeMC9dEbCwP1I7rH35Ki5hGW/C\n8gSsdsKU6ZcxPsBHwNJEZVGADQGrKzNeEbCwO9MGrMF9oYDlSVi+ONQ/nme6P21T7n0NCo6k\niqh8JCqLAiym28+/WMAqOZb4iFdJ6YqAhf1RE7BMcwzPtYQ3DlkD1q2lYcD661z2VVpt6v2k\n8qGoLAqw0BewnOvJB6zxopnxaraA9XGsqt+jOX6ntxPbBRDFErAyPzdXHrDqAOTYiRUMWKNg\nZJrOrB9q9HU03hO2ASofisqiAIvp/gxdKmCl9DtaNjNezRWwvurZIof6m7lFExYDFpJZ/57K\nS1gCAcsZfFxxaBCwuh+GtAasZ3uRAWsLJ2lQOjSoLAoYM55rRU3lt+ZeLa7B0oCVE6/mCliv\n5rP6Mcfq07ymNxTXBRDFE7Cee3sSmnIEktiAVb3kBKzHFyn2AlZzLT0g9aZwEbCmo7IoYIyA\n1ZeXrmYLWPUOrB9zroS/4IwBC8kGMaJz9a9zOC2jpaR7Q0uEdjc5A1ZGPiJgzURlUcCYvoDl\nWSuqwaRezfDiCgLWyXwRsLA4Z8DqxKq4hLVIwHqs1Vvb3P4pO9K5oSOEsw4N3++nevaDOZ0D\nEyAYr7AOQvPS7SsTsAqrG6/yan6+zKHiECEWZw1Y1+t//TMaRCSscUDqrhXcOCMOIvp67cUh\nc/+/JGHZPoS4WvMNDZejefIPb4xXWAepienWVcUDVlSLab2awQXlAeurHnze6x1YX+kNxXUB\nRBnGovb68Jyc4eOXCJcAACAASURBVIS1ZMAa7m8y5QHLO0d+beYbGs7m8PnTXPr9OtTTINwY\nr7AO2wtYiZ2uLGBVH7eh5/iZ3k5sF0CEUSpyTDWPSFgiASs50Bjr2lIBayP5asah4WB+Hpd/\n6t30boxXWAWpeen2VbMa865EwJoGAxZSxQasiI8SjprqrRK7Byuhw+5q9oCVpzODi4CV3NNw\nsqln0YlLAURMG7CyWlsoYLU/lQesk3fPeTYGLKRyBKzYMzNUt3POWVsaNBLaOscBK2Vu/XBG\nuhEJWFvJV+zBArJtL2CldrmygCX74UFrF0AMR8BKcPvGz9AOrPSAdUtY4ZDVCVjdW0veDPc5\n8puJVzPPwfr6bS4xBwvbIDVvyrGi/PGw5MMFsR2uJGAdzSW9gbQugBjDPT/pW1Gzo+elPU9C\nR0LAak9jNW4iMmAJDoFV4QwulWYcGl47nyI8esc5xiusgdBOJ+eKMwUsE1og3OJjNeUB63J6\nlf0WwnEXQASpscMSsIbJyLRLxq0ejYAVYc6h4fvcnAfrcHrnPFjYAH0BK/loQNXfp5/b41oC\nVudvvPSG4roAIiSPHb0PBhr7ZX9XjoRVGrAk0xABaxYqi8KWiGximwhYpnsrASsLAxYSZQSs\nZ8Iyj1gVtR1bd2F5Y1eUdg+WYBwqmSGvk8rHo7IobInIb9ipA1b2lPP4JYzp3pgbX57rKQ9Y\nE2HAQqL0P6h6Aev2zo0cxGwBy/RvzQpJ8vubCFizUFkUNqQdocpbibktt63UxiIWN9arxn5v\ndJ8ELCCJbZO5RShnXnkkrJS9V53luw139lvnnzd9ggN6E33MdzkLPR7Og4Ul3Q9sFW5oggHL\nvlrSH6gZAWsQrLJq7+0C0x+wvk7NFz7/prcT3QUQYt1i7gnKFVgeBwkzd2wPTwlxHwQFApbk\nLqyNUROwjJlofgQwUrDLZtxI+MbMtmIDVkI+MvYrZnxnrN4cLvUB6/U2vJiDaMJiwEKanID1\nSFjFAcuM/s0MWOa2LgHLSeUDUlkUtqNk0pGlleCNmW1F78FKyEfGenkvAevDvF7qgPVh3tIb\niusCCLPFmnYHlTuvdANWQqqxBazHGUolAlbGunuhcmhQWRS2Y1MB6zHjNbWjYdbKK31VAetg\nLvd5/aJjDAMW0tgDVmTY8cUa6+lBLTMvBQMWPFQ+QyqLwnYMd92UthK+Na+thKN+sYPdBAGr\nu57ygPX46BUBC0vyBaxQ2vFGooiA9cxnz3d93l4oJvMEzfgMXc71FxC+H415/fQvycuGSakL\nWK6VEqZVRfbrCFj5f42uKmAd73uwfswxvaG4LrB1EnOOLLHmGo1mCVjd1U1hwMpZaV/me4p+\nD9eR7XK4zWJ/9S7K64YpuUJGfjPBW7OaSgpY6V3JBKz+n7HKA9Z9DtbXwXykNxTXBbZOIGA5\npmAlBCz3Rw2d3VlWN0X5iu0+bL6n6M2cLtd/3n6vWeuNL3vGcmQCVsFRveiVpgxYlokZWXor\nKg9Y1cnE/IVX1AU27qU8Ydl3YAkELPs3NDsDFgf5pjbf82vqL7I3t2+zv5iDd9F5KsJODScf\nlbcSc3tOWzGNEbBSVqnPg2VOgTkKZV1gq9psUpywXPuNojak9IA1/pOSgDWTOQNWVX+Kp3PF\nvegM5WC3LDMSipspbLEgYCV3ZwY/RakPWJNgwNqHx6+tJQOWaUKUvQJHvhoFrOEpsTCVOQ8R\n/lTVe/1PvQfLu4ueFx0T0hew3KsQsOzFJyBgQYjYeQlcO6GiA1baDqzusUe21VnN93T/mMP5\npzodrgnr62i+fIuyDWBCBKys9aIoD1idb4t49U4Dze8Cm2UqqZe6bM6lK0a57+jseWNbndWM\nT/fX4Tm6vXuXZBvAdIznWn47RS16Vgm2RsBKWKX3hVzeeaDZXWCzxAJWyR9UTcByJqlAuwSs\nuc36dH++HeuB7fQe+CIwtgFMR2hyd9EgGb+GfMC6r7HLgFW9Hep959e/9b6rk/+jzNldYKvM\n4x+JhhLv6S7xlxyxHgGLTXVeKp9vlUVhIwhYmevF+Kc7YJ1vc0CrH/NaXeRONsqAtQtib5zy\nKQEErJVQ+XyrLAobsa2AlZs4JnqP/ctNWCm1p+kfIuxckPuIOgPWLogdXB+30Oalzmz06HUT\neiRgzU3l862yKGzDcONSELC8KwRayylfbrLuiPKAdXjswToQsJDm9io/pzHln6shGLA8bROw\nVkXl862yKGzDaOPK3NoIWDb/chNWQumJ+ocI2zlY5+pT7nTuDFh7MAxY2QnLsrk8jvgFw9tw\n5b9WTJ/3gCXwZYqIo3JoUFkUtmH6gJXcIgFrtknur8+vyjFy30fIgLUHwgGru/YzHoUC1mjd\nxIDlbx3SVA4NKovCNggFLN9a2gNWJXbCxJF/uQkruvJk/VVuX5VT78YKnCsmvwts0zOjFB4j\nFA1YSX1mr45MKocGlUVhE8bblvKAVXSvc6UpA1ZWwoquPNkMowkD1h48j65NH7CcbROw1kXl\n0KCyKGyCwoBVso8qt3gCliQGrB3oZBPpgNU5vucNWI/Dkxk9m+e/5Kv5qBwaVBaFTbBsW5k7\ngXLvTF16fQErJ2FFV56MgAUJwgHLvgPL2/ZLG7ByOiZgLULl0KCyKCxNZLMgYBWsFqY9YL0f\n2y/KSW8osgtsU3ffUdGRNt8OLE/Aenkp2YFFwFqGyqFBZVFYmsgvRSUBy1gvpremM2BlRKzp\nCu+u8v78JsL0huK6wEZ1s4lswLLcO765yVelAYspWHNTOTSoLApL0xSwSmeedx5LTsAynvsW\n9S83YUW2XxiwDnKnZnB1gY0yjsuZDaUFLPNSvOvMVP2QiDmoHBpUFoWFGYkNw9qC+MSeiMyU\nEJFsAcu471vUv9yEFdl+4Uslu+PK2gW2yTivZLWUdqp2054itCAhmXs7Oesil8qhQWVRWNiK\nAlawxedjieh7vIhJWHte/3ITVmT7hS/VyVzSG0jrAtskHLBS7jbP+VMFHd9XJ2HNSuXQoLIo\nLKxwfHk2Enejf6nygNWddZramElYe17/chNWZPuFAev38Pqd3kJSF9gm47lWizmdumtd/92d\nnd0lGxoBawkqhwaVRWFhnVmahY1E3The6nl8KXikKer+6MQ4XMj0/9HkX27Cimy/+BAhk9yR\nxR+wBt9X44taqWNH53rRVnv/q4yANSuVQ4PKorCwxQNWb199RjfDu6OPea4oYGUnrMjmCVhY\nRihgDa66d2dFBqw2CEkemiRgzU7l0KCyKCxLZtaRffWYRu+hyMT9Gelf5vFYsgJW55nQ9075\nl5mwIpuXny4nQd/LAGH292BrHKbcESu4aj9hyW1bBKwFqBwaVBaFZYkELMfaKZEpb6dTSVur\nCli5CSuydQIWFnF7iR/pZLCbyYqABZ1Dg8qisKzEUOJvJO7m5GVil059DPbDE9N94U2Jf3kJ\nK7L14oD1dar3QJ5+09uJ7gIbNAhYUQnL19JDIGAJbloErAWoHBpUFoVlbShgJT8ExzyMic7q\nVOZfXsKKbL00YL3epl+Zg2jC0vg6QJRYwHq5u1+17OWyBCyZVMRmOj+Vz7nKorAsM7pQ0kjU\nzcnLRC696YCVmbAiGy8MWB/m9VI/ax/mLb2huC6gTP6+pnErBCykUfmcqywKizKWSyWtxN2e\ntkjs4kUBy3VZjWHAiotYkY0XBqyDudxiKZ8i3AvTnr28KKSMck52wOpvK9ZpWt3OCFjrpvI5\nV1kUFiUSsJyrhtssmzZVVUnfPuhrTf+bIythRbZdGLCaw4MErB0xj6/xkw1YeclndH6QWQMW\n5qdyaFBZFBYlEjGWC1gm6dsHPa2t4L0xDlgRESuy7cKAdbzvwfoxx/SG4rqAJp1p3YsFrFuI\nenmxnHzN9znDTsAiX62WyqFBZVFY1KoD1m1kLZimv/qAFUxYkW3LzMH6OpiP9IbiuoAi3Y/N\nTRWwgt+PU58Qyxhr98ETObADa+VUDg0qi8Ki1hawLAXvJWDZE1YgY0U2XRiwqtP9PO6v6e3E\ndgE9TDOp/Ha5PGD1WogPWLeTjiZ0T8DaDpVDg8qisCTH5+hKWom8J7dPSyI0o3uSG1vFW8MR\nsLwRK7Lp0oDVnAfLnD7Tm4nvAlrcdmBlz0fvN+S4KeILnk0V/UXQw94IWCuncmhQWRSWtOaA\nNUhHWdUX7P1agDNhuSNWZMvFAWsS63hVdue+22magHW/LSY4mcjlLN0xBWvlVA4NKovCkkQC\nlme9UJPpXdqO6pn+1YzW1vHWcAcsZ8SKbJmAhViPcFK+G8gXsOLryOiOLWvlVL6AKovCkghY\nmWUswhewHAkrsuXSgPVxrKrfozl+p7cT2wWUEDyuLhiw/v7c3wM97o4ta+VUvoAqi8KSjOda\nZiNJLRb8Yh/OqNhBwPInLGvEimy4MGB91Z/nPNSz3EUT1lpell2RTClLBSw2rLVT+QqqLAoL\nMt6rma2ktCgTsOrLRbWv5p2RnLAi2y0MWK/mszkH1qfsxwhX87LsiWDAsjfQ3BoZsNKOTz5m\njbFhrZ3KV1BlUVjQ5AEr1KSOgLWeN4Y/YFkyVmS7hQHrdpLRc8WZ3LfPHrCSJpv3GhhlpNvc\n9ZRC0jpkdvsGqBwaVBaFBQ23iLwtZJGANTy4uY+AFU5Yg4wV2axAwDqZLwLWDgwPzTeSTpfQ\nX98asCJCUM7GQcDaCpVDg8qisCCRgOVdyd9iQX+CAWtN74uIgNXLWJHNFh8i/PkyhyrlEOHH\n0ZjTl3hVmJixXc6KV/6AFUxBBKw9Uzk0qCwKC1pvwJLZ91aVHF1cRlzC+jdvwPqq57e/1zuw\nApGpandyvd7O/H6WrgoTcwSs/KYWC1jErBVTOTSoLArLGW8QOb9oCVizikxY/+Y9TcOhyUrH\niFO5N9vL2ZwvVfV79n934bpemH3oTi1v80onX6Wf93Occ+KOERKw9kzl0KCyKCwnO2A9Q1Vw\n0k1B/PKtJLYtZx9cXEpswLplrMhGSwNWynr1igdzqS9fzHGKLjCZ3lG9++vzR8DCzFQODSqL\nwnLyA9b112Qzeym8vHUJ47szpkW5TXl1ASslYf37F9nm3AGr3XBKdn9iAfaA1Ykqyd8NmBmw\nSj6PQ8BaPZVDg8qisBzLBhG3jdx2IkV9ZMy2zCPUZI+Sgpuy7AffZqAxYCWcyb15vt/aDeAg\nXBWm1Z+XbpkuNWvASs5IBKyNUDk0qCwKy8kNWCkbkr0Pk9yObX0R63tX6AtYKWdyN+b0/vFl\n6tlal7N/lvv6XprN607Bss9Hj05Yzhx1a2HCgBV3DBKKqRwaVBaFxdh3LmWuGL2sec6hyg5Y\nklvy+t4V+gJWypnczV1z8XARrgqTGsQagYBlQcBCiMqhQWVRWMwsAWu4cPfgoIqAtULqAlbS\nmdx/fj4+TqdmqvvZm6/2/jIrFBGwohNWIGClVRKpO+wQsFZM5dCgsigsxjv/PHnFuIVN90LR\nPOk90xiwOJP7DqgJWLk7oZ7DDvlqzVQODSqLwmJyA1badmQcVwpmUu1+Q9YWsDLO5J7aBRQY\n7TYqyCqefBU9BpUELKyZytdQZVFYin1zIGCtgbKAlXIm98wuoMDoBck7hbu9rWebBCwEqHwN\nVRaFpcwUsPrHkrqX2R7z6QpYKWdy7zfi7ZgNRBkCFnRQ+RqqLAo5JF5KRxvhpvMDVn9vFttj\nPmUBK9d4GzBdEl1AzvAFKchX3ilYkWNQxqHJe8BiAtbKqRwaVBaFHBK/e5YOWGyPJbYRsBbv\nAgnkd2A5zoIVfOHztwyTnc2giMqhQWVRyFAwf6nXSMLNCQu4l2cLlKMyYH2f0htK7AKLsezA\nyn6JvMf4vHfWNxOwdk7l0KCyKGSQmEngWl/+r0djuYRSqgLWeZKjemwuciTOTRAfsMK7tiIC\n1vjeRzYiYO2cyqFBZVHIYB7/FLaRcHv8As4V2AAlKQpYz3wV/SnCj6Mxp8DSbC9ijCuzpLQx\nuO47mBdMWHkBq50+RcDaOZVDg8qikMF0/i1rI+WOyPvdK7ABitITsA7ms3o1v7+vUd9FWP/7\nestj3q8iZHuR00aT0oA1/F5nVxSKC1jOauzxyzzmp5vsx0HA2gSVQ4PKopDODH4WNRJ/R26v\nBKyJqAlY9a/vd/NV/UR9F2FV7/KqvyXn92w+hKuC1SOaFASLYTBpMpRzx1ggYQWOWLoC1j1Z\nmetdmQ+EgLUJKocGlUUhnUTAcq8baLXgdzEboCxVAeurDksRc7CaRQ6m+RbCizkKVwWrRzRJ\nCxYvrXsbltUzd2FFBazB/c9kZAoSEhvVFqh8FVUWhXQrDVhsf9K0BKyT+ax+r2HpOzZgtctx\notFZNE95YcBy7PjJ3IWVG7C6WS8vYrFRbYHKV1FlUUgncczNs6q/VQKWIkoC1lcdlJppVW/h\n9eoV39pN4iBcFWye0ST/0Jh9B1ZRwHKcBcvR6n0VUxGwoPJVVFkUkhnLpYJGUu7K65OANRkd\nAat6v6WmwKT123rm9P7xZeov1bmc/SuwwcjopJnYVDI644YrEbVLpSUs5ysbCFj3UzQwjWrv\nVA4NKotCskUDVlaXJn9VeCkJWCnrPU+YZczhMkUX6OvsfIoOWNUgZDl2YMUHLOO8YltpvECn\nFLaL3VO5CagsCskkApZvTQLWiqwuYFU/Px8fp1Mz1f3szVdsMDJy9veMpnm6Apb7GOFwuUcZ\n1/8JWCiichNQWRSSGevF7Dbi7iuaWG+y10SIjoD1eaonYEWfZjSnC2S6Z6OkZ3M4zdOZr+ID\n1qON2zwqq8der9ESxnEZu6RyE1BZFFKJDDWJe6mufzSakt1Q7cxUyNMQsO7nDTWiX0XIFiMi\n50+j0d9wg5U7h/9im30GLE8YiwtY2D2Vm4PKopBqgYDVGWQJWOosH7DO5lDvvPo6+E8cWtIF\nchUGLOt7Nytg1f+1AcuRsZwBi00BXSq3B5VFIdXsAct0hujMDglYU1o8YB3MT/Pzx3/i0JIu\nkGl4sC9hpXsKGr/te/PX49q9/3V2+xjgi+scC8+Gh2NQVCfYC5Xbg8qikCru4zgJbQTu7R4u\nyJ1fmh/NEGHpgPWM4KKvMptMOWO5FLtWm4JGr2puwGrOdmrc57By7hhjS0CPyg1CZVFIJDLy\nBFZzZ7jcbciw9U1p8UOE7R4s0UlYbDLlJAKWdwdWasCKLKM/d970ysHuqRwaVBaFRMsGrFwE\nrGktPMn9vZmD9X0If9dzdhfIMZpPEJdSBgFrID5gjQ75pQasznfjELDwoHJoUFkUEs0dsGS2\nGgLWxBY+RNiT3phYVeh7fHKvsqSmP+fJ1r0Ba7hWVMJqW0yYE9+pgYCFHpVDg8qikEgiYIXW\nmiBgsfFNjICFkV4wsQUse8bqH58bsgcs+8Lu8y6EdGvw71DD/qgcGlQWtTelL8Jw/az25g9Y\nbHyTW/IQ4TTYZkr5A5YzYvkDVtLS7lOzJ7TKDiz0qRwaVBa1M8V/3pcHrJh9DMZ6sQQb3+SU\nBCz2YKnRDyb2/UDKA1b7/c4ELHSoHBpUFrUv5VORygJW7AEc+YCF6RGw0GMLWDFBJe2QXMwB\nxYy/A6tnswQs9KkcGlQWtSfNr57CV6EgYCXMjjGWS9CPgIWnQS4JBKyMs7P3Fi8OWINdac9y\nmYKFAZVDg8qidsR0/i1rw3+LY82UjglYK0XAwsNwx88zqNimtv85T6Me1Y//GGF5wCJf4Unl\n0KCyqP0wvR9ljXhviV0zamE2mnUhYOFulEseAcv+2cHnfHfJgBXdovvsD2wHGFC5SagsajfM\n4GdZK75bIleMW5yNZmUIWLhxBCz3+a/ahJX6vEcHLO9eKAIWoqncJFQWtRsELMyCgIWae6hw\nnl/0Hr3sz7v7tKQR8YmABUkqNwmVRe2F0HBhWTmuvcyAxTazQgQs5AWsyhmwXOckdXRlX8IX\nsMatMwbBZfZt4uNozOnLvwwb6oJkApZtXQIWBghYcAcsT75yrVn54hUBC3Obb5u4DWevt++o\nOPsXnaUgWC0csDKnVbDNrBQBa/ecO7vjAlY3DPnjVcQLFTFLi4CFeDMHrLM5X6rq92w+vIvO\nVBLGjPViSTNp7SV3KvKZRyyGgLV3roAVzFfWgJXcl+1+T8Byn0+ezQAjMwesg7nUly/m6F10\nloJgM2HAimowM2CxyazWYgFLDltfgdLZBEnnnfI3/PcXsQcrUAinwULHzAGr/aPR/8cj49Vy\njONyfitp7RGw9me+gGWeXv3TFLK7QCJ3wAplFfGA9dg9lRWwTLMWAQsdMwestzZgHbyLzlAO\nrIzzSn4zKe2ld0nAWr8lApbxj0HZXSCRLSbF7Ugy988MhmZexTd8byc1JBGw4DBnwDq9f3yZ\nz+vFy9k/y53xajEELCxgtkOEb4f6E8xfB/NdnQIftcntAmlmDViRCSsRAQsOcwasm+bi4eJd\ndKaSMGQ81/LbSWiQgLVPMwWss/lpfv6Y19BE0NwukMh6oC/q6F/GIcJpAlbTqmkaJV+ha8ah\n4efn4+N0aqa6n735ivFqMcZ7NbeZhPYyf4GyxexE8SHCzgU+RaiCJ2AF4oq2gFW3SsBCl8qh\nQWVRu7B0wMrpkIC1I4UB6/DYg3UgYOlgT0lRk6FMeBFHd661TMExQgIWxlQODSqL2oPhE0/A\ngi7FhwjbOVjn6tO8LlgV7rwBK+JrA7O6yw5YjrsJWLBTOTSoLGoPpg5YwQYJWPAqneT+2p6k\nod6B5T3b8cRV4W7mgOU/rlgcsMhX6FloaOA8WCoJBSz3agQsFCkNWNXXydy/DNW8y5Q06gIp\nrIEn6oyfkwSsAFf+MmwDsFETsHpnqFmiJFg2hpIxLO2eou7YYPaiOGBNgu0vn3Ui1SNgBdfM\n688fsNypzrl/izEIVio3C5VF7QABC8oRsLbG+txNHrC8dxKwIEXlZqGyqBUofd6mD1iOu4z3\n3nB3bDB7URywPutZWKdPoXKsXSCF7bm75pgFAtY1VxGwIEvlZqGyKP1KD61aVi/5oE78fY/R\niYAFP8FJ7oLY/rI5dmDFPKdiAaudmv7yEghYnhnwbAKwmX27+Dje55h6sLFmWX3Ayp5Tzwaz\nF4UB6+NxmgaxTxAOu0ASxw6siOc0tLcptkfzQsDCVObbLm6//u9/Qfq/BYyNNYcpfOIc2Ueo\nIc+dj48B5pbP9rIbhQHr+DjRqNjX5Ay7QBLnUzdTwDLmkasebb04gpTvFA5sArCZOWCdTf0t\nOb9n/x+QbKw5Vh2wnilLukNsSWHA6n1Vjpy9b4AFZ3/K/kCMSMBqNgNbwMr7xhxgYOaAdTDN\ntxAGvmd17+NVltSEMjwbhn/6eWIhKfc+518RsBAgtgfrIFPPuIsdKjm9ZjBgOdsWCFhtE+1N\nj0OFBCzImDlgtb/UOdGouOSA1WQs073uaDWu78hVPAGLlx0hzMFSKT9hGefqg9TjuD83YDXr\nPS72wlz9LwkLImYOWG/tb1PvH5C7H68yJE8TN70frjUjA1Zvt3tUv+PrnF8WQaV7VPkU4SSy\nA5YnJU0bsJoV7QGrxkFCiJgzYJ3eP75MfQaay9k/y33341WG3IA1DFquxQJthfaEuRuMXxMo\nPmT9eeI8WBKamDqavZTejGf1QNu5AWsYq55Jq9sYCQsS5gxYj6/BMeZw8S46U0kbEohJzhWq\n9thteDl/Y4E9Yc4Gea2RQHxOoIgdbsT3Q3uh3UxRzWQFrOx8Ndpv9byt+zoSsCBgxqHh5+fj\n43Rqprqfvflqj+NVqYKA5Z9fHtNiJ6GFFydgIR8BS4l27lThLixLTHokG1d4e2lOXJX/nMcF\nrD7iFrKoHBpUFqVa9P6j0Rq3K+71YgNW/DHKhBnxQF9BwDJ9C1e1cu7ZS5ntPD2zjL3tF5mA\n1dn9VvWGMCsCFrKoHBpUFqVZxjwm47kWe1d/Ee+RRleDvNRIQcDSod2BNTiqljxzKStgFb6A\niQHrL+NhATcqhwaVRWlWHLDKFnwcHoydsJVRBlBxiFCLR8DqPPacJJIYsG4z6xNrtfc5yG3O\nPw//CFjIp3JoUFmUYqO5BGnrFC+YdoDSOC4DQQQsHewBK68ZV74az9c0o6Wz2ObHG8ftQAmV\nQ4PKohTLCFiZk7VKGxsuziuNJAQsFTpR5PHYe/kqMmxZnjhfwHp0Wsb2gRwCFqagcmhQWZRe\nOcfcEp7i8KIELMyEgKVCN+q0D34QsKwJa3h0LiNgCegGrG4pprpNoRfqBtA5NKgsSi8CFvaC\ngKWC5TD/IFHZE1a7Xhtixk9cb7XoT+Kk8QWsoi9WBAZUDg0qi1IraxSSDFipL1fGlHygQcBS\nIWIepS1hNR+DqQNMZMCa6AMxpvMvAQtTUjk0qCxKrdUFrOcKvNBIQ8DSwDbkjHKJJWE9Atbw\n8GJUR9MGrPZkgOQrCFI5NKgsSqvhk5X+Ub7SZQlYmAsBSwPr33QRCavZS7R8wLq1NJwyz5fN\nQ57KjUplUVqtOGDxOiMRAUsD6+Tz8a6fYcBqPql3X2xwiodAT8NTmhYiYGEmKjcqlUUpNXqu\nop68pGeYgAUtCFgaRAYs62rjgOVbsTMrXjhgmd5ksG5fgBiVG5XKopRaY8DqfYwHiEfAUsCx\n0zyYsHr7jJ47pVIClswMqVvAqhsjYGFSKjcqlUUpNUPACi1NwMJcCFgKjKLO7VhgKPz0V1MR\nsJjRjmmpHBpUFqWT5amKefZUBCxeZqQiYClQFrDM4Bb/es+9Y5PswQImpXJoUFmUTgoCVvbv\nPF5mpCJgKVAQsPpzqW63PFaznZu0swsrpo9IhoCFWagcGlQWpdM6A1bnYzxAAgLW8kb7nf7+\nvHuX7rnp8SR1L7y8JAUsqUhk2rQHTErl0KCyKJ3yAlbqE+xdnoCF2RCwlmfZgeV9Au7nw3IF\nrM5yrs4qAhbWSeXQoLIonWxPVfjpUxGweJWRjIC1vGHAugYj/xNwS1jPZczg57MdV28ELKyT\nyqFBZVEqSs9QHgAAHnFJREFUWZ8pAha2ioC1vOSA1SSs0dz24Zk97fmq/4ljAhbWReXQoLIo\nldYasO6zTIE0BKzFDaPOYPeU1V//KOI135jRidMjApZYIjL7esmwGJXbmcqiVJopYHlXyAxY\nvMhIR8BanDXqhJ6BQcCyLO7IV/09WGJ29YphOSo3NJVFqWR/poLPHwEL60TAWlzeH3XBBVwB\n674mAQtrpHJDU1mUSgoCVt6LRcBCDgLW/AZ7q/IDVt4RPgIW1kvlhqayKJXyAlb68ysesPju\neuQgYC2gF4x8Q447QRVMoTLuXgHlVG64KovSyPVEBZ5AiYD1CEi5AStvNewbAWsB0QHLHaEK\nPrRHwMJ6qdxwVRal0WwBa7iKeR7iI2BhPgSsOdlik+Ox+ndhFX0G0Nz+56QKWB+VQ4PKojRa\nKGCZ7h+VvFiYDwFrTpaA5R9yfAGrvu/vLrmKgj1gwHJUDg0qi9LI+UT5n8Gy31Kmn6x4sTAf\nAtaczChhDYLOMyp5A9ZjB1ZhwCJhYWVUDg0qi9JomYDV/8mLhfkQsOZkDVj2rw/0TsJy7X+K\ny1vmkdAIWFgZlUODyqLEmZuSFjLuCd0ZXMkMbtrHiwUdCFgzenyhzCPZOPOVN2C5ZmD9Re7Q\nMgQsrJTKoUFlUeLK84mGgLWP1wpKELBmZNrJ5W2yGeSr3slBPccISydQGWdEA3RTOTSoLEpa\n4afwAqv6WiVgYa0IWDN6BKzn9cqVrzwBq/jZ4azEWCuVW67KoqTNH7CMKTgqaQlYj9mnwEwI\nWDOyBKxegLIELEczhXVs9PnF9qncdFUWJW3mgFU228teLgELMyNglYs+1HZ7f3cnYLl3YOV+\n4Ca6EGCFVG66KosSNpwrXtRE8E6BvwFtHxo0+3itoAYBq0CbjmITVj9gjWZSEbCAAJWbrsqi\nhGUFLOO5lr9oUt8ELCyIgFUgMWDd51h2A1bX4MN/rudgJc8NMAWVm7/KooQZ68X4lULrDYNQ\nMQIWlkfAKvAIVnEJqx+wgo/RvsBKnhpgEiq3f5VFCcsJWCYlNg0nS5Uytpb4fA9mRcDKcvtw\nS07Acu7AcixuuZHTK2C3VA4NKouSlRV/FAasHbxUUISAlaUp8OWlrTMlYPVjVnDx8W2cHxT7\npXJoUFmUrJwjeMMP7c0bsNojBv3bdvBSQRECVpZ7wKqSElbvT6rwGpYFyVfYOZVDg8qiZAkE\nrNBaAp9THLc3bGoHLxUUIWDleOyFyghY9/d9dMDqtm3IV9g3lUODyqJE5XzGb3iMbomANWpp\n+y8VNCFg5cgKWKb7MyJgjXdhMQELe6dyaFBZlKjRXPHodZQFLGBOBKwc7RHCpEq7AWu4K8r6\n/czDgGV614AdUjk0qCxKVEbAMr0fEStJB6y6me2/MlCNgJXDNxRYs1JvUTMKWH8xASt6djyw\nWSqHBpVFSco50mYGP8PrjNYoRMDC0ghYOTwzN+1ZqbekGR7rc6xjC1jkK+yayqFBZVGSMgLW\nKFfFryIXsDb/wkA5AlYOd8By56tnQBq+713rWPdgAXum8l2gsihJJQFrfKwwtAoBC1tBwMpg\nHJcrzwFC98QtZybrByzlzwkwB5VvA5VFSRo/wPgJVe1k9+iAJfZsErCwNAJWBuO8EspXloAV\n2udlvQLsk8q3gcqiBFkeX0LAqoNO3Ak+h587LMVpRbEwAlYGZ/DphKW/YXByzVEPZjLbFWCf\nVL4NVBYlKD1g9Yeu2OdHPGCJtQRkIWBlsAafOjp1wtLf3WC5pEnqBCygT+XbQGVRggoDVmI/\nBCxsBgErQ//zfN2E1UPAAoSpfBuoLEqO9eF5H3PuE2IK1gX0IWBliAxYlpUST7PgOR0EsEcq\n3wcqi8oUu7eKgAUEEbDSDaPS4HQKkWv5Jl8NWn5c5CxY2DmVQ4PKojLFfmDQ95iznw8CFraF\ngJXOEbAC8aefkP5Gk+DdPVlWB/ZJ5dCgsqhMoxnpjgdHwAKCCFjphlknImD109Rw/ru/p/bs\npP4egD1QOTSoLCrP+NxRrgfnftAFTwenrsKmELDSjbJO+BhhP0/FpateyzkzuIDNUTk0qCwq\nzyjhOB8bAQsIIWClswasa2Tyxp/4UDXqioAF3KkcGlQWlcdEf3g5I3nFdL+h5xIgYCUbZ52Y\ngGUijwra+iJgATcqhwaVReUZBCzPIyNgASEErGTj2VD3gBVai4AFFFI5NKgsKs9gmnnGVPay\nJ2NDTyUwb8D6fj+Z2un8PVUXM7B+jjmYnTIfUn96FwELO6dyaFBZVJ5+wMo52RUBC2jNGLAu\nR/P0OkkXs7AUZ2J2YJV0dktW5CvsncqhQWVRWczjn94F97KRtwK7NGPAOpvD509z6ffrYM5T\ndDGLgoCVnpDCH1AEdkTl0KCyqFr792z8Cp1/swKW2qcCWMCMAetgfh6Xf8xhii5mYQtYkUcI\nCVhAEZVDg8qiaqb3I3qFyNWsf2oCeJgxYPX+jvL/UaX5bWqrbbqANfiTEtg3le8ElUXV4nZF\njVbIDVgJu8qAPWAPVipbbeGPBxKwAAEq3wkqi6qiJ1ON1+hPxQo2n9oLsBPzzsH6+m0urXoO\nlnUP1u2HJz+VBSzNzwcwI5VvBZVFVdEfBxyvkRWwtD4LwGLmPE3Da+dThMfLJF3MoK5tFJRC\nCSv/NFYELOBJ5VtBZVFVRsDq7vKKWMU4rwCo5g1Y1fe5OQ/W4fS+4vNg5Qesl6yp6v0T0wC7\npvKtoLKoioAFLGzWgKWpi2wlASu3v4LVgS1ROTSoLKpfVlyJnYAVswIBC/DaX8AqzCn2rBN3\niDC3w/wDjMC2qPw1rrKoooAV94HA9A6AXdlRwGoDSllQyQpYJY/HtDvNCFiAyt/jKovK2cGU\nekzRWC8CuFkqYC1wHqzlAlbZwzElM7iATVH5e1xlUWUBK7kHpc8BsCQ9Act0SXQxbPsRUIqS\niiVg1WfB8h7FI2ABMlT+HldZVEbASn4cBCzAZx+HCPupaO6AVfhojK1PYJdU/h5XWVTGaarS\nH4cZXQDwsIuA1QaU0FT02LYGDTwDlrv3kh4Zu4A7lW8GlUURsICl7TFglSQsS2XN9+S4K7ae\n1qG0T2CfVL4ZVBY1qipcJQELEDV/wPo4GnP6mrQLa3MELGD15nwzfL83J0Y2p/MqT4xMwAIW\nNmPAuh3qun9fjverCKcKWALHCJMDVnm+AtCa7xf55dj51M2rd1GV6WL8MaL0VeJ7UfkUAAub\nO2CdzflSVb9n8zFFF57WmpBT3u64hSZfOVu+n8KquF8A1Zy/yM/m8PnTXFrnl9OnB6ych2Hy\nVwU2b+6AdTDNtzxfzHGKLkKtTRewHE2TrwBJ8/0mP5ifx+Ufc/AtqjJeELCApc0dsNqPxM15\nolHJk7WMGrjnK3vLnF8BEDXfb/LeELXAiZFLjYsKlUnAAmTNHbDe2jfkfH8RGsfl0ras9/TT\nFBOwAFHswYo1T8C6r6TyGQCWNmvAOr1/fJnP68XLecY5DYUBqxeQ3LukbJ9QZAcWIGvWOVhf\nv82lVc7BstQ0XcDS+AQAy5s1YD2+BseYw2WKLoKNzRqwGHUAYTO+qV47nyI8zjdeCSFgAYub\nMWBVPz8fH6dTM9X97B2vRN+vxnMtRnbAYtABpM35rvo+N+fBOpzeV3gerPSAlfkoTP6qwMbN\nGbCW6cIasKKO25nxop6DfqOWGXQAaSrfVRqLImABi9tJwHrEHttUKeea4znqCQGLMQcQp/Jt\npbAo96ea01aJ60nhEwAosLeAlbILqyhgMeQA8lS+rxQWNWvAUvj4AQ02H7CGx/niA9Zt4Bgf\nIeze1J4Fa9wwYw4gb6H31erOg5UesLIfhNH4+AEN9hqwIhJWs+v7vtj9R2rA4hQNgCg1Act0\nLVGSX3LAyn8MBCzAYR8Ba3RyquiAVfWWHjU2DljOfgEUU/m7XPa0MiKZLTVgFfRHwAIcth6w\nxp8ETApYg4Q1rKuTr6wfVyRgAaJU/i6XDVgiTc4ZsFS+JoACBCz/ms+A9WKpyx2wLKd4AFBK\n5S/zKU4rU9amY21no0W9qXxNAAV2EbAsnwSsXv7uAjX0dmEN6uqvTMACpjb7L/OPozGnL/8y\nqw9Yk3QG7N5uA1YVGbC6Ccu7A4uABUxuvl/mtyNf9+/L8X4V4SQBa5KdSqk7tgCU2HjAsjUU\n2TgBC1Bn5oB1NvW3ev2ezYd3UcFeZRpNSlLkK2AaBKzgms9JW94jhAQsYHIzB6yDab419WKO\n3kUFe5VpNCVgka+AiewwYMW1/jy2GD3kdUMVHyIEJjBzwGo/ITfbiUaN9WJJM6GbyVfAVLYd\nsAr2iHcSkrHc5mnX+nlDAAJmDlhvbcA6eBeV61Sm1YRPCzJSAZNZdcByz1D3tkPAAlZqzoB1\nev/4Mp/Xi5ezf5Y7AQuAxcoDViBh2dsZrzW+ZXS4b3CbpzcCFjCVOQPW45Tqxhwu3kXlOs1q\ndrRgfMBioAKms+qAFUxY1nbalXpfKThsp7ezynR/RAUshi1gCjO+s35+Pj5Op2aq+9mbr5YP\nWMMlowMWAxUwoXUHrG4yeq7ziEDWRHRdxVTDO0YJi4AFKKTynTXVh3Ii2x1/GWBswFL5bAKb\nsfKA1UlGzV9xTfp5eel+N/M4YFXjgDVKWDkBq7MAAxcwBZXvrMUDVvSKBCxgRmsPWM9k1PwZ\nd0s/bcKyJaJ6cUvAsp40dLArzNzjm2X54VoMXMAUVL6zlg9Y0ccWjecaAFmrD1ht0rnNRW0j\nUXrAsnxx8/P+e8BqbokPWJwGCxCmMhJIFZU5BZ2ABei0/oDVW+WRaZ67kSwxynQW6tzTiUzW\nvySbgNWu4w5Yj0sELECYykiwbMAynX+Dq+XNogeQY1sB6+Wlm52cASu8C8s2afQxx2u4sGUt\nAhYwBZWZYLKAFdVyb4poaC0CFjCfrQWs8Uf5bDHHGrB8/ROwAA1UZgKhoizNELCAFdtqwHq2\nIhKw2g/q+APWcz0CFjAFlZlARcAa/n0X0YfKJxPYjq0ELMsH+Nz5Kti+M2D5prhXw6GOgAUI\nU5kJFg1Yxn0h1InKJxPYjk0FrP6X1ER/lCbmfgIWoIDKTCBTlLWVcNPjHVcELECHzQSs8Snd\nfY34O7Dda7oBy/UNPQQsYFIqMwEBC4DFhgLW84yj4UYiAtYgHo2+7svd7P2zjOQrQJrKTKAk\nYFmmu8csDmAimwlY9XmsOuccHbcxPpGo1eNEpPkBi2gFTERlKMgpyvpJ5YymLXukCFiADhsJ\nWM0KbcSaJGDF1cSxQWBKKkNBVsAaruRoJGm+qH3oc62g8rkENmRLAas9G3s7ygS/a9Dq78+e\nkghYwOJUhoK8UdSMbslpexywAmsQsIC5bCtgda+ZXtD5G8xLdyeh+5J5IYmABUxJZSjIHEXN\nOBylt03AAtTaasBqYtLLy/ObA/+sK9gTluuezt3eOgwJC5iEylCQPYpGTIiKjkuPqwQsQIlt\nBKzhpKnblPcmYd1uGKUi33T0ZmECFqCPylCQ86Gc4ZqzBazn/SqfS2BDthqwbudteHGeF9QT\nsIw3YHnzFQELmJTKUDBlwIqesv64HhuwVD6VwJZsM2BVpuqetyExYLnuqLpN+ippAhYhCxCn\nMhXkB6yItEPAAtZqqwGrucWXhtwJy915OF91ZpkSsABxKlPBcgFrfGf4hH0ELGAm2wlY/UAT\nO8okBazISghYwERUpoKSD+WYUBMELGCtNhGwLIEmP2CN1gzutRqtTcACpqEyFZQHLF8LifeF\niwlmOgAi1hywHhEmJ9DEBKy/VmKzBCxgGipTQUnA6gwZGa0TsADF1hywHhmmIGB570iOV1Xn\nc9IELECcylSQNWe0dyUzYOU9GwQsYB6bCVjJecbVR+HDe3yKh4AFiFOZCooC1vNvsvTWSwKW\nymcS2JRVB6w2xGRV5Fip9NERsIDpqIwFxQErcSJ7dsfdtVQ+k8CmbCFgFe0nt95cEI5uo+Xz\nS3oAyFEZC3I+lNO77m8gZjpDegEqn0lgUwhYtpuLAxb7r4ApqIwFBCwAFusOWLccIxGwHrmK\ngAXopTIWFAas0Pri00UJWMAsNhCwiv6Me1y5p6Lyw3uGgAVMRWUsIGABsNh9wHrMkzcELEA7\nlbEgraj0hyD+gZzQBxcBSFh5wKoKDsjdO3kcZTT3gFUYjghYwGRUxoJlAlbBUxH64CIACQSs\n5zQucw9YZQhYwGRU5gICFgCL1Qes/Enpo4B1vSjw2EzpNHkALipzQVJRYkMuAQtQbhMBKzPN\ndCZhEbCANVCZC2YNWMZ2Y3qDKp9IYFvWHrBK0kxnF5ZgwGLkAiaj8t2VOqWhqANjChp6Nqjy\niQS2ZQsBK3dv0TNg9T5QWIqRC5iKynfXnAGr3flU9kQQsIAZrDxg3fKVUMASwsgFTEXluyt1\nzmhJB6bzfz4CFjCDTQSssl6kAxaAqah8q84dsMrnUBmVzyOwMesOWIWlmNEFAJqpfKsmzhkt\n6uB2sTggqXwegY0hYJU3A2AmKt+rkwes8d+CBCxAv1UHLKlBhsEGWAeV79WkKQ1lPUg9fpXP\nI7Axqw5YUt0w2ADroPK9usKABWB6BKz5ugNQSOV7dfopDQQsYIV2HbDafkrOVgpgPioDxnwB\nS+XDB2BHwHqexn2mTgHkUpkwZpgzKnH6dgDzImBd/22yFQELUE9lwphvSFT58AHYEbDqf+tw\nRcAC1FOZMAhYACwIWPeARb4C9FOZMGYbElU+egAO+w5Y7fdOELCAVVAZMeYoyjz+AbASBKz6\nfwIWsAoqIwYBC4AFAYuABayGyohBwAJgQcC6BSzyFbACKiPGXAFL5YMH4ELAuu/BAqCfyoxB\nwAJgsfOAde2p7ouABayCyowxS1FG6YMH4ELAYtACVkPl25WABcCCgMWgBayGyrfrTAFL5WMH\n4ETAYtQCVkPl25WABcCCgMWoBayGyrcrAQuAxd4DFoMWsCIq36/zFGVUPnYATgSs+boCUEjl\n+3WmgDVLLwDEELDm6wpAIZXvVwIWAIvdBywA66FyaFBZFIClEbAArIbKoUFlUQCWRsACsBoq\nhwaVRQFYGgELwGqoHBpUFgVgaQQsAKuhcmhQWRSApRGwAKyGyqFBZVEAlkbAArAaKocGlUUB\nWBoBC8BqqBwaVBYFYGkELACroXJoUFkUgKURsACshsqhQWVRAJZGwAKwGiqHBpVFAVgaAQvA\naqgcGlQWBWBpBCwAq6FyaFBZFIClEbAArIbKoUFlUQCWRsACsBoqhwaVRQFYGgELwGqoHBpU\nFgVgaQQsAKuhcmhQWRSApSkNWABgMf3ok27p5wSAThmjifwApcYKHhslilhBjZQIJ7XPPIUl\n0loXhaUSqkvrw5OwgsdGiSJWUCMlwkntM09hibTWRWGpCFhBK3hslChiBTVSIpzUPvMUlkhr\nXRSWioAVtILHRokiVlAjJcJJ7TNPYYm01kVhqQhYQSt4bJQoYgU1UiKc1D7zFJZIa10UloqA\nFbSCx0aJIlZQIyXCSe0zT2GJtNZFYakIWEEreGyUKGIFNVIinNQ+8xSWSGtdFJaKgBW0gsdG\niSJWUCMlwkntM09hibTWRWGpCFhBK3hslChiBTVSIpzUPvMUlkhrXRSWioAVtILHRokiVlAj\nJcJJ7TNPYYm01kVhqQhYQSt4bJQoYgU1UiKc1D7zFJZIa10UloqAFbSCx0aJIlZQIyXCSe0z\nT2GJtNZFYakIWAAAADoRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAA\nAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIQRsAAAAIRtKGB9\ntI/lfDCvX80lc9PeejhfFqrtLlDix1F9iVffi28zgRp/3ox5+12otjt/iRelG2P3qdNQ4kap\nHanUjk9aRyW1I5Ha8UfrqBOoK3vTX/yXpZif9s322mxH77ebHtvU7dbjggUGSzw3lw6L/lIL\nlHh1OSy9zQRq/FL/NP4ebiUuGgItJXafOg3vl41SO1KpHZ+0jkpqRyK144/WUSdQV/6mv/Qv\nSzE/h/bPLPN6qS5v5qd+1k7t3d/m8FMv871YgcESf8zbpb7vbbECgyXWTmbhbSZU4+H6Sl9O\n5rxUfVWwxLemuLO6V7rz1Gl4v2yU2pFK7fikdVRSOxKpHX+0jjqBugo2/a0ErOsTc3+KXpuX\n57d+Xj5uSbR2NvVuv8/nDfMLlXi63blkfgmVWNVP4cIBK1TjZzN6XMxhofqqcIlG6SvdeeoU\nvF82Su1IpXZ80joqqR2J1I4/WkedUF0Fm/5WAtb1yehvNua1ft4+2vtPpt4fOvizZ16hEtvF\nFnxJwiX+PjbFpYRqvP31sahQiffDGUtmQGuJnadOwftlo9SOVGrHJ62jktqRSO34o3XUCdXV\nLrbjgPUzzOX1j5P5ejOH8+DWpYRKvLnUr+1SwiW+mt+FA1aoxqOp3g/NLt3FhEp8v++iX3D3\nkLXEzlOn4P2yUWpHKrXjk9ZRSe1IpHb80TrqhOq6ydr0NzSA3p+bY5OCv2/bVOO10vILw1vi\nzYf5Wqi4G3+J7+Zz6eewCr7SzZUF9w5VVehp/KhnmR6G+wZmNi6x89TpeL9slNqRSu34pHVU\nUjsSqR1/tI463rpusjb9DQ2g96fo3Zwu1c/r7Sn6rD+SWu8b1fELw1ti4/ew8EEZb4nNztvl\nf+kGXul6buLbwrOH/K/0+/OjKrpKfDx1Ot4vG6V2pFI7PmkdldSORGrHH62jjreuRt6mv6EB\ntH1Zms+gdj5Vcqk/9qnjF4a3xObCYcEDhA1vicf6g6rL/9INvNL1ofPfhc8w4C3xo95Ff33r\nLrsLa1xi56nT8X7ZKLUjldrxSeuopHYkUjv+aB11vHXVMjf9DQ2g7VN03XIO790Xqb54UPEL\nw1ti7XXxEw/5Snxr9pEu/0vX+zTqiAbeEo+mPrB/UZIBnyV2njod75eNUjtSqR2ftI5Kakci\nteOP1lHHW1ctc9Pf0ADae1l+OltPfcft8wm/C38qylvitbzj68InIPeXaB7mr6sr8EqPl5mf\nt0RdGbDRlNh56nS8XzZK7UildnzSOiqpHYnUjj9aRx1vXQWb/vYC1qGJ5x/1i3S72Lxe782f\nOV+Lnn4yUOK1uqWPD1b+EpUFLN8r/bvwc+kt8faH2qKn6qpsJXaeOh3vl41SO1KpHZ+0jkpq\nRyK144/WUcdbV8Gmv72A1Zyg9vtYT+k7N8eam7OX6TgztbfEpTPBjbfE7hILCjyNx+ZcvJ96\nS7xevNxvUFVi56nT8X7ZKLUjldrxSeuopHYkUjv+aB11vHUVbPqL/7KUc3+KLrcvWjo9L95P\nStL/uPEivCW+qdg95H8WO0ssyF/ju/pX+v6FV+pK7D51Kt4vG6V2pFI7PmkdldSORGrHH62j\njreugk1/8V+WctqH/3t9Ok63P2zqbw0/fjwuHpY+4OEtccE93R3+Z7G7xHICNX69Kn+l718a\nv1BpLUuJnadOxftlo9SOVGrHJ62jktqRSO34o3XU8dZVsOkv/ssSAABgawhYAAAAwghYAAAA\nwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAA\nwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAA\nwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAAwghYAAAA\nwghYAAAAwghYAAAAwghYAAAAwghYmIbpuF5ZuhwAAObELz5Mg4AFANgxfvFhQgQrAMA+8QsQ\nEyJgAQD2iV+AmFAbsOqf1//fzeG9qs7GnJtbP47m8LFgdQAATIWAhQn1A9Z7PR/r67X+t05Y\np2Z+1uuiBQIAMAkCFibUD1ivl+rj/u+hqr7qS5dX87VsiQAATICAhQn1A9Z3c+n3fv1kLtdL\nF3NasD4AAKZBwMKEBnOwqu6/z5M4AACwNfx2w4QIWACAfeK3GybkD1jL1QUAwLT4JYcJ+QLW\nientAIDNImBhQr6A9WkOP1X1wSR3AMAGEbAwIV/AqpoTYpnD72LVAQAwFQIWJuQNWPWZ3M0b\n+QoAsEEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEE\nLAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEE\nLAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGEE\nLAAAAGEELAAAAGEELAAAAGEELAAAAGEELAAAAGH/A5fTw+rUjdA0AAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title \"Forecasts from Holt's method\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"#\n",
"plot.ts(log_passengers)#, main = \"Double Exponential smoothing\")\n",
"lines(fitted.values(d_es), col = \"blue\", lty = 2, lwd = 2)\n",
"lines(fitted.values(forecast::holt(log_passengers, alpha = 0.1, beta = 0.09)), col = \"darkorange\", lty = 2, lwd = 2)\n",
"#\n",
"plot(forecast::forecast(d_es, h = 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Triple Exponential Smoothing (Holt-Winter's Method)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"t_es <- forecast::hw(log_passengers)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAOVBMVEUAAAAAAP9NTU1oaGh8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\nYQQsAAAAYQQsAAAAYf8DGqm09Ra65NcAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title \"Forecasts from Holt-Winters' additive method\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"#\n",
"plot.ts(log_passengers)#, main = \"Triple Exponential smoothing\")\n",
"lines(fitted.values(t_es), col = \"blue\", lty = 2, lwd = 2)\n",
"#\n",
"plot(forecast::forecast(t_es, h = 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`R` allows to use an automated procedure to choose the smoothing parameters - the function `ets` selects the best variant automatically (by the minimum of AIC) and estimates its parameters:"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"ets_es <- forecast::ets(log_passengers)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAOVBMVEUAAAAAAP9NTU1oaGh8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\nAADCCFgAAADCCFgAAADCCFgAAADC/gdWMgxTUVeWYAAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"Forecasts from ETS(M,A,M)\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"#\n",
"plot.ts(log_passengers)\n",
"lines(fitted.values(ets_es), col = \"blue\", lty = 2, lwd = 2)\n",
"#\n",
"plot(forecast::forecast(ets_es, h = 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note the help file:\n",
"\n",
"- The first letter denotes the error type (\"A\", \"M\" or \"Z\"); \n",
"- The second letter denotes the trend type (\"N\",\"A\",\"M\" or \"Z\"); \n",
"- The third letter denotes the season type (\"N\",\"A\",\"M\" or \"Z\"). \n",
"\n",
"In all cases, \"N\"=none, \"A\"=additive, \"M\"=multiplicative and \"Z\"=automatically selected. So, for example, \"ANN\" is simple exponential smoothing with additive errors, \"MAM\" is multiplicative Holt-Winters' method with multiplicative errors, and so on."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(ets_es$residuals)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals ppear to have a *slight* autocorrelation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## SARMA models with trend"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"tt_dt <- data.frame(tt = 1:length(log_passengers))\n",
"tt_dt$tt_sq <- tt_dt$tt^2\n",
"#\n",
"mdl_auto = forecast::auto.arima(airpass, max.d = 0, max.D = 0, xreg = tt_dt)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: airpass \n",
"Regression with ARIMA(0,0,3)(0,0,1)[12] errors \n",
"\n",
"Coefficients:\n",
" ma1 ma2 ma3 sma1 intercept tt tt_sq\n",
" 0.9875 0.7195 0.3621 0.7592 117.1154 1.5895 0.0068\n",
"s.e. 0.0822 0.1077 0.0914 0.0668 20.7197 0.6575 0.0044\n",
"\n",
"sigma^2 estimated as 359.3: log likelihood=-630.18\n",
"AIC=1276.35 AICc=1277.42 BIC=1300.11"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_auto"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAABNTU1oaGh8fHyM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",
"text/plain": [
"Plot with title \"SARMA with trend\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(airpass, main = \"SARMA with trend\")\n",
"lines(mdl_auto$fitted, col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can examine the residuals"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(mdl_auto$residuals)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that there appears to be a large autocorrelation for every `12`-th lag. So the restriction of no differencing causes `auto.arima` to fail to find a suitible model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For somparison, if we were to specify a $SARIMA(1, 0, 1)\\times(1, 0, 1)_{12}$. If we use the default specification, we may get a warning that the series is not stationary:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"tryCatch({\n",
" forecast::Arima(airpass, order = c(1, 0, 1), seasonal = c(1, 0, 1), xreg = tt_dt)\n",
"}, warning = function(w) {\n",
" # warning-handler-code\n",
"}, error = function(e) {\n",
" print(e)\n",
"}, finally = {\n",
" # cleanup-code\n",
"})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we are sure that the process is stationary, we can specify a different parameter estimation method:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"mdl_manual = forecast::Arima(airpass, order = c(1, 0, 1), seasonal = c(1, 0, 1), xreg = tt_dt, method = \"ML\")"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: airpass \n",
"Regression with ARIMA(1,0,1)(1,0,1)[12] errors \n",
"\n",
"Coefficients:\n",
" ar1 ma1 sar1 sma1 intercept tt tt_sq\n",
" 0.7540 -0.1003 0.9630 -0.1336 119.0055 1.4857 0.0077\n",
"s.e. 0.0724 0.1045 0.0161 0.0925 38.2025 0.5299 0.0033\n",
"\n",
"sigma^2 estimated as 128: log likelihood=-564.67\n",
"AIC=1145.35 AICc=1146.41 BIC=1169.11"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_manual"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAABNTU1oaGh8fHyM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\np5n2GiiSPQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"SARMA with trend\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(airpass, main = \"SARMA with trend\")\n",
"lines(mdl_manual$fitted, col = \"red\")"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nBCwAgGACFgBAMAELACDY/wdM8Jupvu6H4gAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(mdl_manual$residuals)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals look much better compared to the `auto.arima` results with restriction that the data is not to be differenced."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we can forecast the process. we do need to have the soem future values of the trend. Thankfully, we have opted to use the standard indexing of $t = 1,2,...$ for the trend."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"tt_forc <- data.frame(tt = tail(tt_dt$tt, 1) + 1:20)\n",
"tt_forc$tt_sq <- tt_forc$tt^2"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAALQCAMAAAAjXrvTAAAAPFBMVEUAAAAAAP9NTU1oaGh8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\nAElFTkSuQmCC",
"text/plain": [
"Plot with title \"Forecasts from Regression with ARIMA(1,0,1)(1,0,1)[12] errors\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(forecast::forecast(mdl_manual, xreg = tt_forc))\n",
"lines(mdl_manual$fitted, col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"----\n",
"----\n",
"----\n",
"\n",
"# Time series with unit root"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 15)\n",
"options(repr.plot.height = 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# (1) Series plot and transformation"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"suppressPackageStartupMessages({library(forecast)})"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"nyse <- read.table(url(\"http://uosis.mif.vu.lt/~rlapinskas/(data%20R&GRETL/nyse.txt\"), header = TRUE)\n",
"nyse <- ts(nyse, start = 1952, frequency = 12)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Jan Feb Mar Apr May Jun Jul\n",
"1952 100.00000 101.55801 98.35478 102.49584 97.45797 99.92923 103.53153\n",
"1953 107.99719 107.70146 106.74088 104.92693 101.94905 101.89004 99.83214\n",
"1954 102.88020 108.08621 109.38209 113.14183 117.91136 120.87454 121.79292\n",
" Aug Sep Oct Nov Dec\n",
"1952 104.61471 103.15134 100.79363 100.10055 105.16128\n",
"1953 102.22141 97.10542 96.98586 101.49628 103.35702\n",
"1954 127.93562 124.25727 132.08256 129.77409 141.50459"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(nyse, 36)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAAJ1BMVEUAAABNTU1oaGiampqn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",
"text/plain": [
"Plot with title \"~\"",
"Plot with title \"Delta\"",
"Plot with title \"log(Y[t])\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 3))\n",
"plot(nyse, main = bquote(Y[t])) \n",
"plot(log(nyse), main = bquote(log(Y[t])))\n",
"plot(diff(log(nyse)), main = bquote(Delta~log(Y[t])))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the growth appears to be exponential - it is more convenient to take logarithms to *linearize* the series."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"lnyse <- log(nyse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# (2) $\\rm ACF$ and $\\rm PACF$ plots"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nJggBaJogBKBpghCApglCAJomCAFo2v8B4SbiVfIOBn0AAAAASUVORK5CYII=",
"text/plain": [
"Plot with title \"Series lnyse\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"forecast::Acf(lnyse, )\n",
"forecast::Pacf(lnyse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Slow ACF decay - indication of non-stationarity, or a trend, or a nonstationarity and/or drift and/or trend. **We need to test whether the data is TS or DS. To do this - we need to carry out unit root testing**.\n",
"\n",
"We can always load the relevant libraries to avoid the use of `::` notation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"# (3) Unit root testing"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: zoo\n",
"\n",
"Attaching package: 'zoo'\n",
"\n",
"The following objects are masked from 'package:base':\n",
"\n",
" as.Date, as.Date.numeric\n",
"\n"
]
}
],
"source": [
"library(forecast)\n",
"library(dynlm)\n",
"library(urca)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## (3.1) Manual Unit root testing\n",
"\n",
"\n",
"Unit root tests consist of:\n",
"\n",
"- Selecting the lag order of the autoregressive model $\\Delta Y_t = \\alpha + \\delta t + \\rho Y_{t-1} + \\sum_{j = 1}^p \\gamma_j \\Delta Y_{t-1} + \\epsilon_t$\n",
"- Determine whether the trend coefficient, $\\widehat{\\delta}$, is significant;\n",
"- Dependin on the final model, asses whether $\\widehat{\\rho}$ is significant.\n",
"\n",
"\n",
"### Lag Order selection\n",
"\n",
"We will examine three cases:\n",
"\n",
"- Starting with $p_\\max = 4$;\n",
"- Starting with $p_\\max = 5$;\n",
"- Starting with $p_\\max = \\biggr\\lfloor 12 \\cdot \\left( \\dfrac{T}{100} \\right)^{1/4} \\biggr\\rfloor$;\n",
"\n",
"#### **Starting with $p_\\max = 4$**"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Time series regression with \"ts\" data:\n",
"Start = 1952(6), End = 1995(13)\n",
"\n",
"Call:\n",
"dynlm(formula = d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:4) + time(lnyse))\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-0.220902 -0.024758 0.001637 0.026627 0.152618 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -2.3687707 1.1485800 -2.062 0.0397 *\n",
"L(lnyse) -0.0172567 0.0083590 -2.064 0.0395 *\n",
"L(d(lnyse), 1:4)1 0.0544182 0.0439376 1.239 0.2161 \n",
"L(d(lnyse), 1:4)2 -0.0282788 0.0439795 -0.643 0.5205 \n",
"L(d(lnyse), 1:4)3 0.0150921 0.0439341 0.344 0.7313 \n",
"L(d(lnyse), 1:4)4 0.0364522 0.0439285 0.830 0.4070 \n",
"time(lnyse) 0.0012584 0.0006077 2.071 0.0389 *\n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"Residual standard error: 0.04061 on 517 degrees of freedom\n",
"Multiple R-squared: 0.01244,\tAdjusted R-squared: 0.0009837 \n",
"F-statistic: 1.086 on 6 and 517 DF, p-value: 0.3696\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:4) + time(lnyse))\n",
"summary(mod.1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The last lag coefficient, `L(d(lnyse), 1:4)4` is insignificant since its $p-value = 0.4070 > 0.05`. We will reduce the maximum lag and continue the procedure."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.2563 1.1441 -1.9721 0.0491\n",
"L(lnyse) -0.0162 0.0083 -1.9420 0.0527\n",
"L(d(lnyse), 1:3)1 0.0514 0.0439 1.1689 0.2430\n",
"L(d(lnyse), 1:3)2 -0.0274 0.0439 -0.6227 0.5338\n",
"L(d(lnyse), 1:3)3 0.0151 0.0439 0.3438 0.7311\n",
"time(lnyse) 0.0012 0.0006 1.9789 0.0484\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:3) + time(lnyse))\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`p-value` of `L(d(lnyse), 1:3)3` is `> 0.05`."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.2314 1.1372 -1.9621 0.0503\n",
"L(lnyse) -0.0161 0.0083 -1.9483 0.0519\n",
"L(d(lnyse), 1:2)1 0.0493 0.0438 1.1244 0.2614\n",
"L(d(lnyse), 1:2)2 -0.0263 0.0439 -0.6004 0.5485\n",
"time(lnyse) 0.0012 0.0006 1.9698 0.0494\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:2) + time(lnyse))\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`p-value` of `L(d(lnyse), 1:2)2` is `> 0.05`."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.2880 1.1308 -2.0233 0.0435\n",
"L(lnyse) -0.0164 0.0082 -1.9956 0.0465\n",
"L(d(lnyse), 1) 0.0480 0.0438 1.0956 0.2737\n",
"time(lnyse) 0.0012 0.0006 2.0302 0.0428\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1) + time(lnyse))\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`p-value` of `L(d(lnyse), 1)` is `> 0.05`."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.1695 1.1246 -1.9292 0.0542\n",
"L(lnyse) -0.0155 0.0082 -1.8995 0.0580\n",
"time(lnyse) 0.0012 0.0006 1.9362 0.0534\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse) + time(lnyse))\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**The final model contains no lags of $\\Delta Y_{t-j}$ - so there is no autoregressive coefficient for the difference model.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"#### **Starting with $p_\\max = 5$**\n",
"\n",
"We will repeat the procedure as before."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.6325 1.1505 -2.2882 0.0225\n",
"L(lnyse) -0.0192 0.0084 -2.2920 0.0223\n",
"L(d(lnyse), 1:5)1 0.0540 0.0439 1.2319 0.2185\n",
"L(d(lnyse), 1:5)2 -0.0286 0.0439 -0.6523 0.5145\n",
"L(d(lnyse), 1:5)3 0.0208 0.0439 0.4738 0.6359\n",
"L(d(lnyse), 1:5)4 0.0329 0.0438 0.7516 0.4527\n",
"L(d(lnyse), 1:5)5 0.1030 0.0438 2.3508 0.0191\n",
"time(lnyse) 0.0014 0.0006 2.2962 0.0221\n"
]
}
],
"source": [
"mod.2 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:5) + time(lnyse))\n",
"print(round(coef(summary(mod.2)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`L(d(lnyse), 1:5)5` has `p-value < 0.05`, so the final lag order is `5`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"#### **Starting with $p_\\max = \\biggr\\lfloor 12 \\cdot \\left( \\dfrac{T}{100} \\right)^{1/4} \\biggr\\rfloor$**\n",
"\n",
"The maximum lag via the rule-of-thumb is:"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"18"
],
"text/latex": [
"18"
],
"text/markdown": [
"18"
],
"text/plain": [
"[1] 18"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"floor(12 * (length(lnyse) / 100)^(1/4))"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.0342 1.2305 -1.6532 0.0989\n",
"L(lnyse) -0.0152 0.0091 -1.6706 0.0954\n",
"L(d(lnyse), 1:18)1 0.0509 0.0453 1.1234 0.2618\n",
"L(d(lnyse), 1:18)2 -0.0321 0.0454 -0.7058 0.4806\n",
"L(d(lnyse), 1:18)3 0.0307 0.0453 0.6776 0.4984\n",
"L(d(lnyse), 1:18)4 0.0279 0.0454 0.6162 0.5381\n",
"L(d(lnyse), 1:18)5 0.1048 0.0451 2.3241 0.0205\n",
"L(d(lnyse), 1:18)6 -0.0660 0.0453 -1.4561 0.1460\n",
"L(d(lnyse), 1:18)7 -0.0292 0.0454 -0.6423 0.5210\n",
"L(d(lnyse), 1:18)8 -0.0719 0.0454 -1.5853 0.1135\n",
"L(d(lnyse), 1:18)9 0.0048 0.0455 0.1060 0.9156\n",
"L(d(lnyse), 1:18)10 -0.0205 0.0455 -0.4518 0.6516\n",
"L(d(lnyse), 1:18)11 0.0159 0.0453 0.3505 0.7261\n",
"L(d(lnyse), 1:18)12 0.0322 0.0453 0.7105 0.4777\n",
"L(d(lnyse), 1:18)13 0.0164 0.0451 0.3640 0.7160\n",
"L(d(lnyse), 1:18)14 -0.1022 0.0450 -2.2723 0.0235\n",
"L(d(lnyse), 1:18)15 0.0043 0.0452 0.0948 0.9245\n",
"L(d(lnyse), 1:18)16 -0.0426 0.0451 -0.9442 0.3455\n",
"L(d(lnyse), 1:18)17 0.0341 0.0451 0.7574 0.4492\n",
"L(d(lnyse), 1:18)18 -0.0507 0.0451 -1.1236 0.2618\n",
"time(lnyse) 0.0011 0.0007 1.6627 0.0970\n"
]
}
],
"source": [
"mod.3 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:18) + time(lnyse))\n",
"print(round(coef(summary(mod.3)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`L(d(lnyse), 1:18)18` is insignificant. We will continue reducing the lag order untill the last lag is significant. We omit the intermediate model output with insignificant $p_\\max$ coefficients. The final model"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.0920 1.2078 -1.7320 0.0839\n",
"L(lnyse) -0.0151 0.0089 -1.7043 0.0890\n",
"L(d(lnyse), 1:14)1 0.0510 0.0448 1.1383 0.2555\n",
"L(d(lnyse), 1:14)2 -0.0233 0.0449 -0.5198 0.6034\n",
"L(d(lnyse), 1:14)3 0.0283 0.0449 0.6307 0.5285\n",
"L(d(lnyse), 1:14)4 0.0301 0.0448 0.6722 0.5018\n",
"L(d(lnyse), 1:14)5 0.1041 0.0448 2.3227 0.0206\n",
"L(d(lnyse), 1:14)6 -0.0664 0.0451 -1.4723 0.1416\n",
"L(d(lnyse), 1:14)7 -0.0299 0.0450 -0.6637 0.5072\n",
"L(d(lnyse), 1:14)8 -0.0658 0.0450 -1.4631 0.1441\n",
"L(d(lnyse), 1:14)9 0.0047 0.0449 0.1057 0.9159\n",
"L(d(lnyse), 1:14)10 -0.0163 0.0447 -0.3638 0.7162\n",
"L(d(lnyse), 1:14)11 0.0120 0.0447 0.2690 0.7880\n",
"L(d(lnyse), 1:14)12 0.0389 0.0446 0.8727 0.3832\n",
"L(d(lnyse), 1:14)13 0.0100 0.0446 0.2247 0.8223\n",
"L(d(lnyse), 1:14)14 -0.0972 0.0446 -2.1787 0.0298\n",
"time(lnyse) 0.0011 0.0006 1.7390 0.0826\n"
]
}
],
"source": [
"mod.3 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:14) + time(lnyse))\n",
"print(round(coef(summary(mod.3)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"has a $p_\\max = 14$ lag order."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"If we compare the $\\rm AIC$ and $\\rm BIC$ values of the three models:"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | mdl_1 (p = 0) | mdl_2 (p = 5) | mdl_3 (p = 14) |
\n",
"\n",
"\tAIC | -1881.349 | -1860.785 | -1813.996 |
\n",
"\tBIC | -1864.273 | -1822.449 | -1737.636 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" & mdl\\_1 (p = 0) & mdl\\_2 (p = 5) & mdl\\_3 (p = 14)\\\\\n",
"\\hline\n",
"\tAIC & -1881.349 & -1860.785 & -1813.996\\\\\n",
"\tBIC & -1864.273 & -1822.449 & -1737.636\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | mdl_1 (p = 0) | mdl_2 (p = 5) | mdl_3 (p = 14) | \n",
"|---|---|\n",
"| AIC | -1881.349 | -1860.785 | -1813.996 | \n",
"| BIC | -1864.273 | -1822.449 | -1737.636 | \n",
"\n",
"\n"
],
"text/plain": [
" mdl_1 (p = 0) mdl_2 (p = 5) mdl_3 (p = 14)\n",
"AIC -1881.349 -1860.785 -1813.996 \n",
"BIC -1864.273 -1822.449 -1737.636 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"a <- data.frame('mdl_1 (p = 0)' = c(AIC(mod.1), BIC(mod.1)), \n",
" 'mdl_2 (p = 5)' = c(AIC(mod.2), BIC(mod.2)), \n",
" 'mdl_3 (p = 14)' = c(AIC(mod.3), BIC(mod.3)),\n",
" check.names = FALSE)\n",
"rownames(a) <- c(\"AIC\", \"BIC\")\n",
"a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $\\rm AIC$ and $\\rm BIC$ values are smaller for the model, where we started with an arbitraty value of $p = 4$. Having determined the lag order, we asses the trend significance.\n",
"\n",
"Note: we will examine the final models for each case. In reality we would need to select an arbitrary lag outselves, if we opt to manually test for a unit root."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Determining the trend significance\n",
"\n",
"For the 1st model:"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.1695 1.1246 -1.9292 0.0542\n",
"L(lnyse) -0.0155 0.0082 -1.8995 0.0580\n",
"time(lnyse) 0.0012 0.0006 1.9362 0.0534\n"
]
}
],
"source": [
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The trend is insignificant, so we remove it."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 0.0077 0.0122 0.6352 0.5256\n",
"L(lnyse) -0.0001 0.0019 -0.0720 0.9426\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ L(lnyse))\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"For the 2nd model:"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.6325 1.1505 -2.2882 0.0225\n",
"L(lnyse) -0.0192 0.0084 -2.2920 0.0223\n",
"L(d(lnyse), 1:5)1 0.0540 0.0439 1.2319 0.2185\n",
"L(d(lnyse), 1:5)2 -0.0286 0.0439 -0.6523 0.5145\n",
"L(d(lnyse), 1:5)3 0.0208 0.0439 0.4738 0.6359\n",
"L(d(lnyse), 1:5)4 0.0329 0.0438 0.7516 0.4527\n",
"L(d(lnyse), 1:5)5 0.1030 0.0438 2.3508 0.0191\n",
"time(lnyse) 0.0014 0.0006 2.2962 0.0221\n"
]
}
],
"source": [
"mod.2 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:5) + time(lnyse))\n",
"print(round(coef(summary(mod.2)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The trend is significant, so we leave it.\n",
"\n",
"---\n",
"\n",
"For the 3rd model:"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.0920 1.2078 -1.7320 0.0839\n",
"L(lnyse) -0.0151 0.0089 -1.7043 0.0890\n",
"L(d(lnyse), 1:14)1 0.0510 0.0448 1.1383 0.2555\n",
"L(d(lnyse), 1:14)2 -0.0233 0.0449 -0.5198 0.6034\n",
"L(d(lnyse), 1:14)3 0.0283 0.0449 0.6307 0.5285\n",
"L(d(lnyse), 1:14)4 0.0301 0.0448 0.6722 0.5018\n",
"L(d(lnyse), 1:14)5 0.1041 0.0448 2.3227 0.0206\n",
"L(d(lnyse), 1:14)6 -0.0664 0.0451 -1.4723 0.1416\n",
"L(d(lnyse), 1:14)7 -0.0299 0.0450 -0.6637 0.5072\n",
"L(d(lnyse), 1:14)8 -0.0658 0.0450 -1.4631 0.1441\n",
"L(d(lnyse), 1:14)9 0.0047 0.0449 0.1057 0.9159\n",
"L(d(lnyse), 1:14)10 -0.0163 0.0447 -0.3638 0.7162\n",
"L(d(lnyse), 1:14)11 0.0120 0.0447 0.2690 0.7880\n",
"L(d(lnyse), 1:14)12 0.0389 0.0446 0.8727 0.3832\n",
"L(d(lnyse), 1:14)13 0.0100 0.0446 0.2247 0.8223\n",
"L(d(lnyse), 1:14)14 -0.0972 0.0446 -2.1787 0.0298\n",
"time(lnyse) 0.0011 0.0006 1.7390 0.0826\n"
]
}
],
"source": [
"print(round(coef(summary(mod.3)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The trend is insignificant, so we remove it"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 0.0083 0.0129 0.6479 0.5173\n",
"L(lnyse) -0.0001 0.0020 -0.0471 0.9624\n",
"L(d(lnyse), 1:14)1 0.0427 0.0446 0.9574 0.3388\n",
"L(d(lnyse), 1:14)2 -0.0317 0.0447 -0.7094 0.4784\n",
"L(d(lnyse), 1:14)3 0.0198 0.0447 0.4433 0.6577\n",
"L(d(lnyse), 1:14)4 0.0217 0.0447 0.4859 0.6273\n",
"L(d(lnyse), 1:14)5 0.0957 0.0447 2.1419 0.0327\n",
"L(d(lnyse), 1:14)6 -0.0753 0.0449 -1.6792 0.0937\n",
"L(d(lnyse), 1:14)7 -0.0379 0.0449 -0.8456 0.3982\n",
"L(d(lnyse), 1:14)8 -0.0733 0.0449 -1.6329 0.1031\n",
"L(d(lnyse), 1:14)9 -0.0017 0.0449 -0.0374 0.9701\n",
"L(d(lnyse), 1:14)10 -0.0232 0.0446 -0.5202 0.6031\n",
"L(d(lnyse), 1:14)11 0.0051 0.0446 0.1139 0.9093\n",
"L(d(lnyse), 1:14)12 0.0320 0.0445 0.7184 0.4729\n",
"L(d(lnyse), 1:14)13 0.0031 0.0445 0.0688 0.9452\n",
"L(d(lnyse), 1:14)14 -0.1046 0.0445 -2.3500 0.0192\n"
]
}
],
"source": [
"mod.3 <- dynlm(d(lnyse) ~ L(lnyse) + L(d(lnyse), 1:14))\n",
"print(round(coef(summary(mod.3)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, we have that:\n",
"\n",
"- The 1st model does not contain a trend.\n",
"- The 2nd model does contain a trend;\n",
"- The 3rd model does not contain a trend;\n",
"\n",
"---\n",
"\n",
"### Carrying out the unit root test\n",
"\n",
"The $\\rm ADF$ test tests the null hypothesis:\n",
"$$\n",
"H_0: \\rho = 0 \\text{ (i.e. the series contains a unit root)}\n",
"$$\n",
"\n",
"Depending on the trend, the critical values are:\n",
"\n",
"- The 1st model does not contain a trend - we need to compare the t-statistic of $\\widehat{\\rho}$ with -2.89;\n",
"- The 2nd model does contain a trend - we need to compare the t-statistic of $\\widehat{\\rho}$ with -3.45;\n",
"- The 3rd model does not contain a trend - we need to compare the t-statistic of $\\widehat{\\rho}$ with -2.89.\n",
"\n",
"\n",
"\n",
"\n",
"Looking at the 1st model:"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 0.0077 0.0122 0.6352 0.5256\n",
"L(lnyse) -0.0001 0.0019 -0.0720 0.9426\n"
]
}
],
"source": [
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The coefficient $\\widehat{\\rho}$ t-value is `L(lnyse) = -0.0720 > -2.89`. So we have no grounds to reject the null hypothesis and conclude that the series contains a unit root.\n",
"\n",
"---\n",
"---\n",
"\n",
"Since we have determined that `L(lnyse)` is insignificant, we could remove it from the model, **if we wanted to consider this model as a contender for the best model for this series**:"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 0.0069 0.0018 3.8836 1e-04\n"
]
}
],
"source": [
"mod.1 <- dynlm(d(lnyse) ~ 1)\n",
"print(round(coef(summary(mod.1)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then the estimated for $\\Delta Y_t$ is: $\\Delta Y_t = 0.0069 + \\epsilon_t$, which we can write it as a model for $Y_t$: $Y_t = 0.0069 + Y_{t-1} + \\epsilon_t$, which is an $\\rm AR(1)$ model for $Y_t$.\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"Looking at the 2nd model:"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -2.6325 1.1505 -2.2882 0.0225\n",
"L(lnyse) -0.0192 0.0084 -2.2920 0.0223\n",
"L(d(lnyse), 1:5)1 0.0540 0.0439 1.2319 0.2185\n",
"L(d(lnyse), 1:5)2 -0.0286 0.0439 -0.6523 0.5145\n",
"L(d(lnyse), 1:5)3 0.0208 0.0439 0.4738 0.6359\n",
"L(d(lnyse), 1:5)4 0.0329 0.0438 0.7516 0.4527\n",
"L(d(lnyse), 1:5)5 0.1030 0.0438 2.3508 0.0191\n",
"time(lnyse) 0.0014 0.0006 2.2962 0.0221\n"
]
}
],
"source": [
"print(round(coef(summary(mod.2)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The coefficient $\\widehat{\\rho}$ t-value is `L(lnyse) = -2.2920 > -3.45`. So we have no grounds to reject the null hypothesis and conclude that the series contains a unit root."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"\n",
"Since we have determined that `L(lnyse)` is insignificant, we could remove it from the model, **if we wanted to consider this model as a contender for the best model for this series**:"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -0.07357 0.27887 -0.26382 0.79203\n",
"L(d(lnyse), 1:5)1 0.04398 0.04382 1.00357 0.31606\n",
"L(d(lnyse), 1:5)2 -0.03932 0.04380 -0.89786 0.36968\n",
"L(d(lnyse), 1:5)3 0.01035 0.04380 0.23620 0.81337\n",
"L(d(lnyse), 1:5)4 0.02288 0.04376 0.52299 0.60121\n",
"L(d(lnyse), 1:5)5 0.09225 0.04373 2.10951 0.03538\n",
"time(lnyse) 0.00004 0.00014 0.28548 0.77539\n"
]
}
],
"source": [
"mod.2 <- dynlm(d(lnyse) ~ L(d(lnyse), 1:5) + time(lnyse))\n",
"print(round(coef(summary(mod.2)), 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we needed the trend for unit root testing - having removed the insignificant $\\rho$ coefficient, we could try to remove the insignificant trend and improve our model. But we will assume that this model is acceptible as is."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then the estimated model for $\\Delta Y_t$ is: \n",
"\n",
"$\\Delta Y_t = -0.07357 + 0.00004 \\cdot t + 0.04398 \\Delta Y_{t-1} -0.03932 \\Delta Y_{t-2} + 0.01035 \\Delta Y_{t-3} + 0.02288 \\Delta Y_{t-4} + 0.09225 \\Delta Y_{t-5} + \\epsilon_t$, \n",
"\n",
"which we can re-write as a model for $Y_t$. \n",
"\n",
"We use the property $\\gamma_j = -[\\phi_{j+1} + ... + \\phi_p]$, $j = 1, ..., p - 1$ and the expression of $\\rho$ to get the coefficients:\n",
"\n",
"$\n",
"\\begin{aligned}\n",
"\\gamma_5 &= - \\phi_6 &&\\Longrightarrow \\phi_6 = - \\gamma_5 = -0.09225\\\\\n",
"\\gamma_4 &= - [\\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_5 = - \\gamma_4 - \\phi_6 = -0.02288+0.09225 = 0.06937\\\\\n",
"\\gamma_3 &= - [\\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_4 = - \\gamma_3 - [\\phi_5 + \\phi_6] = - \\gamma_3 + \\gamma_4 = -0.01035+0.02288 = 0.01253\\\\\n",
"\\gamma_2 &= - [\\phi_3 + \\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_3 = - \\gamma_2 + \\gamma_3 = 0.03932 + 0.01035 = 0.04967\\\\\n",
"\\gamma_1 &= - [\\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_2 = - \\gamma_1 + \\gamma_2 = -0.04398 -0.03932 = -0.0833\\\\\n",
"\\rho &= \\phi_1 + \\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6 - 1,\\text{ since } \\rho = 0 &&\\Longrightarrow \\phi_1 = 1 - (\\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6) = 1 + \\gamma_1= 1 + 0.04398 = 1.04398\n",
"\\end{aligned}\n",
"$\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, the equivalent model for $Y_t$ is:\n",
"\n",
"$Y_t = -0.07357 + 0.00004 \\cdot t + 1.04398 Y_{t-1} -0.0833 Y_{t-2} + 0.04967 Y_{t-3} + 0.01253 Y_{t-4} + 0.06937 Y_{t-5} -0.09225 Y_{t-6} + \\epsilon_t$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"To verify that this is indeed the correct transformation, we can try to simulate a few observations with the same residuals:"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"N <- 200\n",
"eps <- rnorm(mean = 0, sd = 1, n = N)\n",
"tt <- 1:length(eps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we will simulate $Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [],
"source": [
"Y <- NULL\n",
"Y[1] <- -0.07357 + 0.00004 * tt[1] + eps[1]\n",
"Y[2] <- -0.07357 + 0.00004 * tt[2] + 1.04398 * Y[1] + eps[2]\n",
"Y[3] <- -0.07357 + 0.00004 * tt[3] + 1.04398 * Y[2] −0.0833 * Y[1] + eps[3]\n",
"Y[4] <- -0.07357 + 0.00004 * tt[4] + 1.04398 * Y[3] −0.0833 * Y[2] + 0.04967 * Y[1] + eps[4]\n",
"Y[5] <- -0.07357 + 0.00004 * tt[5] + 1.04398 * Y[4] −0.0833 * Y[3] + 0.04967 * Y[2] + 0.01253 * Y[1] + eps[5]\n",
"Y[6] <- -0.07357 + 0.00004 * tt[6] + 1.04398 * Y[5] −0.0833 * Y[4] + 0.04967 * Y[3] + 0.01253 * Y[2] + 0.06937 * Y[1] + eps[5]\n",
"for(j in 7:N){\n",
" Y[j] <- -0.07357 + 0.00004 * tt[j] + 1.04398 * Y[j-1] −0.0833 * Y[j-2] + 0.04967 * Y[j - 3] + 0.01253 * Y[j - 4] + 0.06937 * Y[j - 5] − 0.09225 * Y[j - 6] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Secondly, we will simulate $\\Delta Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"dY <- NULL\n",
"dY[1] <- -0.0735 + 0.00004 * tt[1] + eps[1]\n",
"dY[2] <- -0.07357 + 0.00004 * tt[2] + 0.04398 * dY[1] + eps[2]\n",
"dY[3] <- -0.07357 + 0.00004 * tt[3] + 0.04398 * dY[2] −0.03932 * dY[1] + eps[3]\n",
"dY[4] <- -0.07357 + 0.00004 * tt[4] + 0.04398 * dY[3] −0.03932 * dY[2] + 0.01035 * dY[1] + eps[4]\n",
"dY[5] <- -0.07357 + 0.00004 * tt[5] + 0.04398 * dY[4] −0.03932 * dY[3] + 0.01035 * dY[2] + 0.02288 * dY[1] + eps[5]\n",
"for(j in 6:N){\n",
" dY[j] <- -0.07357 + 0.00004 * tt[j] + 0.04398 * dY[j-1] −0.03932 * dY[j-2] + 0.01035 * dY[j - 3] + 0.02288 * dY[j - 4] + 0.09225 * dY[j - 5] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we will assume that the first `100`, or so, observations of $Y_t$ are burn-in values (since the first couple of values assume that $Y_j = \\epsilon_j = 0$, for $j \\leq 0$). This means that we treat treat the first `101` $\\Delta Y_t$ values as burn-in values as well and drop them:"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [],
"source": [
"Y <- Y[-c(1:100)]"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"dY <- dY[-c(1:101)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compare $\\Delta Y_t$ with $Y_t - Y_{t-1}$:"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"diff.Y. | dY | DIFFERENCE |
\n",
"\n",
"\t 0.4191779 | 0.4191779 | 0 |
\n",
"\t-0.1389262 | -0.1389262 | 0 |
\n",
"\t-0.5043527 | -0.5043527 | 0 |
\n",
"\t-1.1470432 | -1.1470432 | 0 |
\n",
"\t-0.2097488 | -0.2097488 | 0 |
\n",
"\t-0.7880470 | -0.7880470 | 0 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" diff.Y. & dY & DIFFERENCE\\\\\n",
"\\hline\n",
"\t 0.4191779 & 0.4191779 & 0 \\\\\n",
"\t -0.1389262 & -0.1389262 & 0 \\\\\n",
"\t -0.5043527 & -0.5043527 & 0 \\\\\n",
"\t -1.1470432 & -1.1470432 & 0 \\\\\n",
"\t -0.2097488 & -0.2097488 & 0 \\\\\n",
"\t -0.7880470 & -0.7880470 & 0 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"diff.Y. | dY | DIFFERENCE | \n",
"|---|---|---|---|---|---|\n",
"| 0.4191779 | 0.4191779 | 0 | \n",
"| -0.1389262 | -0.1389262 | 0 | \n",
"| -0.5043527 | -0.5043527 | 0 | \n",
"| -1.1470432 | -1.1470432 | 0 | \n",
"| -0.2097488 | -0.2097488 | 0 | \n",
"| -0.7880470 | -0.7880470 | 0 | \n",
"\n",
"\n"
],
"text/plain": [
" diff.Y. dY DIFFERENCE\n",
"1 0.4191779 0.4191779 0 \n",
"2 -0.1389262 -0.1389262 0 \n",
"3 -0.5043527 -0.5043527 0 \n",
"4 -1.1470432 -1.1470432 0 \n",
"5 -0.2097488 -0.2097488 0 \n",
"6 -0.7880470 -0.7880470 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dt_compare <- data.frame(diff(Y), dY)\n",
"dt_compare$DIFFERENCE <- round(diff(Y) - dY, 10)\n",
"head(dt_compare)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that there is no difference between the simulate $Y_t - Y_{t-1}$ (`diff.Y.`), which was calculated from the simulated $Y_t$ series, and $\\Delta Y_t$ (`dY`).\n",
"\n",
"We can also visually compare the charts:"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nmkYQAgCaRhACAJpGEAIAmvY/AYczfgBJUNUAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(ts(diff(Y)), col = \"red\", lwd = 2)\n",
"lines(ts(dY), col = \"blue\", lty = 2, lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, the two models are equivalent. For simulation and forecasting we may be more interested in $Y_t$ model, as it is the original series, which we are interested in.\n",
"\n",
"## **[INFO: END]**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"The final, 3rd model"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 0.0083 0.0129 0.6479 0.5173\n",
"L(lnyse) -0.0001 0.0020 -0.0471 0.9624\n",
"L(d(lnyse), 1:14)1 0.0427 0.0446 0.9574 0.3388\n",
"L(d(lnyse), 1:14)2 -0.0317 0.0447 -0.7094 0.4784\n",
"L(d(lnyse), 1:14)3 0.0198 0.0447 0.4433 0.6577\n",
"L(d(lnyse), 1:14)4 0.0217 0.0447 0.4859 0.6273\n",
"L(d(lnyse), 1:14)5 0.0957 0.0447 2.1419 0.0327\n",
"L(d(lnyse), 1:14)6 -0.0753 0.0449 -1.6792 0.0937\n",
"L(d(lnyse), 1:14)7 -0.0379 0.0449 -0.8456 0.3982\n",
"L(d(lnyse), 1:14)8 -0.0733 0.0449 -1.6329 0.1031\n",
"L(d(lnyse), 1:14)9 -0.0017 0.0449 -0.0374 0.9701\n",
"L(d(lnyse), 1:14)10 -0.0232 0.0446 -0.5202 0.6031\n",
"L(d(lnyse), 1:14)11 0.0051 0.0446 0.1139 0.9093\n",
"L(d(lnyse), 1:14)12 0.0320 0.0445 0.7184 0.4729\n",
"L(d(lnyse), 1:14)13 0.0031 0.0445 0.0688 0.9452\n",
"L(d(lnyse), 1:14)14 -0.1046 0.0445 -2.3500 0.0192\n"
]
}
],
"source": [
"print(round(coef(summary(mod.3)), 4))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The coefficient $\\widehat{\\rho}$ t-value is `L(lnyse) = -0.0471 > -2.89`. So we have no grounds to reject the null hypothesis and conclude that the series contains a unit root.\n",
"\n",
"We will not re-write this models equations as they can be determined by applying the same methods as before.\n",
"\n",
"---\n",
"\n",
"**Overall, regardless of the lag order we see that the series has a unit root**. \n",
"\n",
"It is important to note, that removing the trend increased the t-statistic of $\\widehat{\\rho}$, so it is very possible that, if we incorrectly remove the trend - we may make an incorrect test conclusion.\n",
"\n",
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## (3.2) Automatic Unit root testing"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will carry out different tests from different packages. For completeness sake, we will provide the same test results from more than one package.\n",
"\n",
"### ADF test\n",
"\n",
"The $\\rm ADF$ test tests the null hypothesis: $H_0: \\rho = 0 \\text{ (i.e. the series contains a unit root)}$\n",
"\n",
"We can set the maximum lag order, and choose the criterion for the order selection:"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"############################################################### \n",
"# Augmented Dickey-Fuller Test Unit Root / Cointegration Test # \n",
"############################################################### \n",
"\n",
"The value of the test statistic is: -2.0965 6.0649 2.2091 \n",
"\n"
]
}
],
"source": [
"tst_adf_1 <- urca::ur.df(lnyse, type = \"trend\", lags = 18, selectlags = \"BIC\")\n",
"print(tst_adf_1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can examine the model"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-0.219561 -0.024529 0.003247 0.026918 0.152312 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 9.001e-02 4.010e-02 2.244 0.0252 *\n",
"z.lag.1 -1.755e-02 8.370e-03 -2.096 0.0365 *\n",
"tt 1.044e-04 5.041e-05 2.070 0.0390 *\n",
"z.diff.lag 5.043e-02 4.444e-02 1.135 0.2570 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"Residual standard error: 0.0409 on 506 degrees of freedom\n",
"Multiple R-squared: 0.01033,\tAdjusted R-squared: 0.004462 \n",
"F-statistic: 1.76 on 3 and 506 DF, p-value: 0.1538\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_adf_1@testreg"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The critical values can be extracted via `@cval`:"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1pct 5pct 10pct\n",
"tau3 -3.96 -3.41 -3.12\n",
"phi2 6.09 4.68 4.03\n",
"phi3 8.27 6.25 5.34\n"
]
}
],
"source": [
"print(tst_adf_1@cval)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To carry out the unit root test, we examine the t-statistic of `z.lag.1` - it is `-2.096` (Note that this is the same as the first value in the output `The value of the test statistic is: -2.0965 6.0649 2.2091 `). The relevant critival value is `tau`, which is `-3.41` for the $5\\%$ significance level. \n",
"\n",
"Since The test statistic `-2.096 > -3.45`, we do not reject the **null hypothesis of a unit root**.\n",
"\n",
"---\n",
"\n",
"The second way to carry out and $\\rm ADF$ test:"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [],
"source": [
"tst_adf_2 <- tseries::adf.test(lnyse, alternative = \"stationary\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can either manually specify the lag order, or let the function select the maximum lag order itself."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tAugmented Dickey-Fuller Test\n",
"\n",
"data: lnyse\n",
"Dickey-Fuller = -1.9019, Lag order = 8, p-value = 0.6198\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_adf_2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This output is a bit easier to read - the $p-value = 0.6198 > 0.05$, so we have no grounds to reject the **null hypothesis of a unit root**.\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### KPSS test\n",
"\n",
"The $\\rm KPSS$ test tests the null hypothesis: $H_0: \\text{ the data is stationary}$\n",
"\n",
"The test involves specifying and estimating the following equation with a random-walk component:\n",
"$$\n",
"Y_t = r_t + \\delta \\cdot t + \\epsilon_t,\\quad r_t = r_{t-1} + u_t\n",
"$$\n",
"\n",
"The null hypothesis of stationarity is equivalent to the hypothesis: $H_0: \\sigma^2_u = 0$, which would mean that $r_t = r_{t-1} = ... = r_0 = \\rm const$ (i.e. a constant intercept).\n",
"\n",
"We can set the number of lags to use the rule of thumb (`lags = \"long\"`, which is equivalent to $\\root 4 \\of {12 \\times (n/100)}$), or `lags = \"short\"`, which is equivalent to $\\root 4 \\of {4 \\times (n/100)}$. The test types specify as deterministic component either a constant `mu` or a constant with linear trend `tau`. "
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"####################################### \n",
"# KPSS Unit Root / Cointegration Test # \n",
"####################################### \n",
"\n",
"The value of the test statistic is: 0.3909 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_kpss_1 <- urca::ur.kpss(lnyse, type = \"tau\", lags = \"long\")\n",
"tst_kpss_1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the test statistic is `0.3909`. The critical values are:"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | 10pct | 5pct | 2.5pct | 1pct |
\n",
"\n",
"\tcritical values | 0.119 | 0.146 | 0.176 | 0.216 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|llll}\n",
" & 10pct & 5pct & 2.5pct & 1pct\\\\\n",
"\\hline\n",
"\tcritical values & 0.119 & 0.146 & 0.176 & 0.216\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | 10pct | 5pct | 2.5pct | 1pct | \n",
"|---|\n",
"| critical values | 0.119 | 0.146 | 0.176 | 0.216 | \n",
"\n",
"\n"
],
"text/plain": [
" 10pct 5pct 2.5pct 1pct \n",
"critical values 0.119 0.146 0.176 0.216"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_kpss_1@cval"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since `0.3909 > 0.146`, we reject the **null hypothesis of stationarity** and conclude that the series is not stationary.\n",
"\n",
"---\n",
"\n",
"The second way to carry out the `KPSS` test (where `lshort = FALSE` indicates to use the rule-of-thumb larger lag selection):"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message in tseries::kpss.test(lnyse, null = \"Trend\", lshort = FALSE):\n",
"\"p-value smaller than printed p-value\""
]
}
],
"source": [
"tst_kpss_2 <- tseries::kpss.test(lnyse, null = \"Trend\", lshort = FALSE)"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\tKPSS Test for Trend Stationarity\n",
"\n",
"data: lnyse\n",
"KPSS Trend = 0.43099, Truncation lag parameter = 16, p-value = 0.01\n",
"\n"
]
}
],
"source": [
"print(tst_kpss_2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since `p-value = 0.01 < 0.05`, we **reject the null hypothesis of stationarity and conclude that the series is not stationary.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### PP test\n",
"\n",
"The $\\rm PP$ test tests builds on the ADF test and tests the null hypothesis: $H_0: \\text{ (i.e. the series contains a unit root)}$.\n",
"\n",
"We begin with the built-in function:"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [],
"source": [
"tst_pp_0 <- stats::PP.test(lnyse, lshort = FALSE)"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tPhillips-Perron Unit Root Test\n",
"\n",
"data: lnyse\n",
"Dickey-Fuller = -1.9395, Truncation lag parameter = 18, p-value =\n",
"0.6039\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_pp_0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`p-value = 0.6039 > 0.05`, so we have no grounds to reject the null hypothesis of a unit root.\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `urca` package also contains the $PP$ test:"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"################################################## \n",
"# Phillips-Perron Unit Root / Cointegration Test # \n",
"################################################## \n",
"\n",
"The value of the test statistic is: -1.9393 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_pp_1 <- urca::ur.pp(lnyse, model = \"trend\", type = \"Z-tau\", lags = \"long\")\n",
"tst_pp_1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Note: use `type = \"Z-tau\"`, otherwise the critical values will be missing!**.\n",
"\n",
"If we are interested, we can examine the specified regression, which was used for this test:"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = y ~ y.l1 + trend)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-0.221927 -0.025066 0.002876 0.026943 0.147915 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 1.045e-01 5.145e-02 2.032 0.0427 * \n",
"y.l1 9.845e-01 8.151e-03 120.792 <2e-16 ***\n",
"trend 9.600e-05 4.958e-05 1.936 0.0534 . \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"Residual standard error: 0.04055 on 525 degrees of freedom\n",
"Multiple R-squared: 0.9981,\tAdjusted R-squared: 0.9981 \n",
"F-statistic: 1.38e+05 on 2 and 525 DF, p-value: < 2.2e-16\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_pp_1@testreg"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although the critical test statistic is calculated differently than the one in the $ADF$ test, the critical values for the PP test are the same as for the DF test. \n",
"\n",
"The critical values are:"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | 1pct | 5pct | 10pct |
\n",
"\n",
"\tcritical values | -3.97979 | -3.420314 | -3.132507 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" & 1pct & 5pct & 10pct\\\\\n",
"\\hline\n",
"\tcritical values & -3.97979 & -3.420314 & -3.132507\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | 1pct | 5pct | 10pct | \n",
"|---|\n",
"| critical values | -3.97979 | -3.420314 | -3.132507 | \n",
"\n",
"\n"
],
"text/plain": [
" 1pct 5pct 10pct \n",
"critical values -3.97979 -3.420314 -3.132507"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_pp_1@cval"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since the value of the test statistic `-1.9393` is greater than the $5\\%$ critical value `-3.420314`, **we have no grounds to reject the null hypothesis of a unit root.**\n",
"\n",
"---\n",
"\n",
"The `tseries` package also has the $PP$ test:"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [],
"source": [
"tst_pp_2 <- tseries::pp.test(lnyse, alternative = \"stationary\", type = \"Z(t_alpha)\", lshort = FALSE)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tPhillips-Perron Unit Root Test\n",
"\n",
"data: lnyse\n",
"Dickey-Fuller Z(t_alpha) = -1.9395, Truncation lag parameter = 18,\n",
"p-value = 0.6039\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tst_pp_2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `p-value = 0.6039 > 0.05`, **we have no grounds to reject the null hypothesis and conclude that the series has a unit root.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"**So, we can conclude that all tests indicate that the series has a unit root.**\n",
"\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 10)\n",
"options(repr.plot.height = 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# (4) Model Building\n",
"\n",
"Since we have determined that the series has a unit root (and we see no indication of seasonality), we can take the differences of the series:"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [],
"source": [
"dlnyse <- diff(lnyse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we examine the series:"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nwA0ICwDc8H9KD6nIluChKgAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(dlnyse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The series appear to be stationary. We will test this by repeating the unit root tests on the differenced data. For simplicity, we will use the test, which have the `p-values`, from the `tseries` package:"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message in tseries::adf.test(dlnyse, alternative = \"stationary\"):\n",
"\"p-value smaller than printed p-value\""
]
},
{
"data": {
"text/plain": [
"\n",
"\tAugmented Dickey-Fuller Test\n",
"\n",
"data: dlnyse\n",
"Dickey-Fuller = -8.1328, Lag order = 8, p-value = 0.01\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tseries::adf.test(dlnyse, alternative = \"stationary\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$p-value = 0.01 < 0.05$, so we **reject the null hypothesis of a unit root**."
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message in tseries::kpss.test(dlnyse, null = \"Level\", lshort = FALSE):\n",
"\"p-value greater than printed p-value\""
]
},
{
"data": {
"text/plain": [
"\n",
"\tKPSS Test for Level Stationarity\n",
"\n",
"data: dlnyse\n",
"KPSS Level = 0.095985, Truncation lag parameter = 16, p-value = 0.1\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tseries::kpss.test(dlnyse, null = \"Level\", lshort = FALSE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$p-value = 0.1 > 0.05$, so **we have no grounds to reject the null hypothesis of stationarity**."
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message in tseries::pp.test(dlnyse, alternative = \"stationary\", type = \"Z(t_alpha)\", :\n",
"\"p-value smaller than printed p-value\""
]
},
{
"data": {
"text/plain": [
"\n",
"\tPhillips-Perron Unit Root Test\n",
"\n",
"data: dlnyse\n",
"Dickey-Fuller Z(t_alpha) = -22.021, Truncation lag parameter = 18,\n",
"p-value = 0.01\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tseries::pp.test(dlnyse, alternative = \"stationary\", type = \"Z(t_alpha)\", lshort = FALSE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$p-value = 0.01 < 0.05$, so we **reject the null hypothesis of a unit root**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In other words, the differences, $\\Delta Y_t$, are stationary.\n",
"\n",
"---\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make it interesting, we will specify three different models:\n",
"\n",
"- A model based on one selected from the $\\rm ADF$ test;\n",
"- A model based on the $\\rm ACF$, $\\rm PACF$ of $\\Delta Y_t$;\n",
"- An automatically specified model via `auto.arima`, without any restrictions.\n",
"\n",
"---\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## - From the `ADF` test we select and re-estimate `mod.2` model (this is a different parametrization than the one on `dynlm`)\n",
"\n",
"Furthermore, we will only be able to estimate the drift component, since if $Y_t$ contais a constant $\\alpha$ and trend $\\delta \\cdot t$, then $\\Delta Y_t$ contains $\\delta$. \n",
"\n",
"In this specification $\\alpha$ is not identifiable."
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [],
"source": [
"mdl_4_1 <- forecast::Arima(lnyse, order = c(5, 1, 0), xreg = data.frame(tt = 1:length(lnyse)))"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Series: lnyse \n",
"Regression with ARIMA(5,1,0) errors \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 tt\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08\n"
]
}
],
"source": [
"print(mdl_4_1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals of this model:"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nSUVORK5CYII=",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(mdl_4_1$residuals)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Appear to be white noise."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"We will now expand upon what a *different parametrization* entails for models specified `dynlm` versus the ones specified with `Arima()`.\n",
"\n",
"#### - The model, specified via `forecast::Arima` (or via `stats::arima`) is specified as a process with a linear trend, whose **deviations from the trend are described as the AR(1) process:**\n",
"\n",
"For example, assume that we would want to specify a model as a stationary $\\rm AR(1)$ model with a trend using `forecast::Arima` (or `stats::arima`) the specification is as follows:\n",
"\n",
"$\n",
"\\begin{cases}\n",
"Y_t &= \\alpha + \\delta \\cdot t + u_t,\\\\\n",
"u_t &= \\phi u_{t-1} + \\epsilon_t\n",
"\\end{cases}\n",
"$"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"stats::arima(x = lnyse, order = c(1, 0, 0), xreg = time(lnyse))\n",
"\n",
"Coefficients:\n",
" ar1 intercept time(lnyse)\n",
" 0.9832 -144.2528 0.0763\n",
"s.e. 0.0076 12.4969 0.0063\n",
"\n",
"sigma^2 estimated as 0.001632: log likelihood = 945.18, aic = -1882.37"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod.a1 <- stats::arima(lnyse, order = c(1,0,0), xreg=time(lnyse))\n",
"mod.a1"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"Regression with ARIMA(1,0,0) errors \n",
"\n",
"Coefficients:\n",
" ar1 intercept time(lnyse)\n",
" 0.9832 -144.2528 0.0763\n",
"s.e. 0.0076 12.4969 0.0063\n",
"\n",
"sigma^2 estimated as 0.001642: log likelihood=945.18\n",
"AIC=-1882.37 AICc=-1882.29 BIC=-1865.28"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod.a2 <- forecast::Arima(lnyse, order = c(1,0,0), xreg=time(lnyse))\n",
"mod.a2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The estimated model is:\n",
"\n",
"$\n",
"\\begin{cases}\n",
"Y_t &= -144.2528 + 0.0763 \\cdot t + u_t,\\\\\n",
"u_t &= 0.9832 u_{t-1} + \\epsilon_t\n",
"\\end{cases}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this case, we would want to test whether the **residuals** exhibit a unit root by testing whether $\\phi = 1$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### - The model, specified via `dynlm::dynlm` is specified as **an autoregressive process with a linear trend:**\n",
"\n",
"From the (1) expression we would have that:\n",
"\n",
"\n",
"$\n",
"\\begin{cases}\n",
"u_t &= Y_t - \\alpha - \\delta \\cdot t,\\\\\n",
"u_t &= \\phi u_{t-1} + \\epsilon_t\n",
"\\end{cases} \\Longrightarrow\n",
"Y_t - \\alpha - \\delta \\cdot t = \\phi \\left(Y_{t-1} - \\alpha - \\delta \\cdot (t-1) \\right) + \\epsilon_t\n",
"$\n",
"\n",
"which means that an alternative specification involves a **reparametrization** of the previous process as:\n",
"\n",
"$\n",
"\\begin{aligned}\n",
"Y_t &= \\tilde{\\alpha} + \\tilde{\\delta} \\cdot t + \\phi Y_{t-1} + \\epsilon_t = \\left[ (1 - \\phi) \\alpha + \\phi \\delta\\right] + \\left[ (1 - \\phi)\\delta \\right] \\cdot t + \\phi Y_{t-1} + \\epsilon_t\n",
"\\end{aligned}\n",
"$\n",
"\n",
"which is as an autoregressive process with a linear trend. \n",
"\n",
"This is the specification that `dynlm::dynlm(...)` uses:"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Time series regression with \"ts\" data:\n",
"Start = 1952(2), End = 1996(1)\n",
"\n",
"Call:\n",
"dynlm::dynlm(formula = lnyse ~ time(lnyse) + L(lnyse))\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-0.221927 -0.025066 0.002876 0.026943 0.147915 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) -2.169524 1.124569 -1.929 0.0542 . \n",
"time(lnyse) 0.001152 0.000595 1.936 0.0534 . \n",
"L(lnyse) 0.984518 0.008150 120.792 <2e-16 ***\n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"Residual standard error: 0.04055 on 525 degrees of freedom\n",
"Multiple R-squared: 0.9981,\tAdjusted R-squared: 0.9981 \n",
"F-statistic: 1.38e+05 on 2 and 525 DF, p-value: < 2.2e-16\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mod.b1 <- dynlm::dynlm(lnyse ~ time(lnyse) + L(lnyse))\n",
"summary(mod.b1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The estimated model is:\n",
"\n",
"$\n",
"\\begin{aligned}\n",
"Y_t &= 2.169524 + 0.001152 \\cdot t + 0.984518 Y_{t-1} + \\epsilon_t\n",
"\\end{aligned}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The models are equivalent, but due to the parametrization $\\alpha \\neq \\tilde \\alpha$ and $\\delta \\neq \\tilde{\\delta}$. The autoregressive coefficient $\\widehat{\\phi}$ also differ due to different parameter estimation methods (which again may further differ for different parametrization options). However they are fairly close: `ar1 = 0.9832` versus `L(lnyse) = 0.984518`.\n",
"\n",
"If we use the parametrization on the estimated coefficients from the first model, we would have that:\n",
"\n",
"$\n",
"\\begin{aligned}\n",
"\\tilde{\\alpha} &= \\left[ (1 - \\phi) \\alpha + \\phi \\delta\\right]\\\\\n",
"\\tilde{\\delta} &=\\left[ (1 - \\phi)\\delta \\right]\n",
"\\end{aligned}\n",
"$"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"-2.34842888000001"
],
"text/latex": [
"-2.34842888000001"
],
"text/markdown": [
"-2.34842888000001"
],
"text/plain": [
"[1] -2.348429"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# tilde{alpha}\n",
"(1 - 0.9832) * (-144.2528) + 0.9832 * 0.0763"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.00128184"
],
"text/latex": [
"0.00128184"
],
"text/markdown": [
"0.00128184"
],
"text/plain": [
"[1] 0.00128184"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# tilde{delta}\n",
"(1 - 0.9832) * 0.0763"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that they are fairly close to `(Intercept) = -2.169524` and `time(lnyse) = 0.001152` respectively.\n",
"\n",
"## **[INFO: END]**\n",
"\n",
"---\n",
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## - Selecting the model based on the ACF and PACF of the series:"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAAM1BMVEUAAAAAAP9NTU1oaGh8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",
"text/plain": [
"Plot with title \"Series diff(lnyse)\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(1, 2))\n",
"forecast::Acf(diff(lnyse))\n",
"forecast::Pacf(diff(lnyse))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can test the lag significance via the $Ljung-Box$ test. The null hypothesis is:\n",
"$$\n",
"\\begin{aligned}\n",
"H_0&: \\rho(1) = ... = \\rho(k) = 0\\\\\n",
"H_1&: \\exists j: \\rho(j) \\neq 0\n",
"\\end{aligned}\n",
"$$\n",
"We will test, whether the first `20` lags have a significant autocorrelation with different values of $k$:"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"lag = 1 p-value = 0.36736\"\n",
"[1] \"lag = 2 p-value = 0.49395\"\n",
"[1] \"lag = 3 p-value = 0.70145\"\n",
"[1] \"lag = 4 p-value = 0.76131\"\n",
"[1] \"lag = 5 p-value = 0.25479\"\n",
"[1] \"lag = 6 p-value = 0.20216\"\n",
"[1] \"lag = 7 p-value = 0.20613\"\n",
"[1] \"lag = 8 p-value = 0.1685\"\n",
"[1] \"lag = 9 p-value = 0.2293\"\n",
"[1] \"lag = 10 p-value = 0.29176\"\n",
"[1] \"lag = 11 p-value = 0.36542\"\n",
"[1] \"lag = 12 p-value = 0.40789\"\n",
"[1] \"lag = 13 p-value = 0.48727\"\n",
"[1] \"lag = 14 p-value = 0.21937\"\n",
"[1] \"lag = 15 p-value = 0.27295\"\n",
"[1] \"lag = 16 p-value = 0.31138\"\n",
"[1] \"lag = 17 p-value = 0.34642\"\n",
"[1] \"lag = 18 p-value = 0.30703\"\n",
"[1] \"lag = 19 p-value = 0.17814\"\n",
"[1] \"lag = 20 p-value = 0.20485\"\n"
]
}
],
"source": [
"for(i in 1:20){\n",
" aa <- Box.test(diff(lnyse), lag = i, type = \"Ljung-Box\")\n",
" print(paste0(\"lag = \", i, \" p-value = \", round(aa$p.value, 5)))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that in all cases the $p-value > 0.05$, so we have no grounds to reject the null hypothesis. This indicates that the differences, $\\Delta Y_t$, are white noise. We can specify the model as:"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {},
"outputs": [],
"source": [
"mdl_4_2 <- forecast::Arima(lnyse, order = c(0, 1, 0), include.drift = TRUE)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Series: lnyse \n",
"ARIMA(0,1,0) with drift \n",
"\n",
"Coefficients:\n",
" drift\n",
" 0.0069\n",
"s.e. 0.0018\n",
"\n",
"sigma^2 estimated as 0.00165: log likelihood=942.79\n",
"AIC=-1881.59 AICc=-1881.56 BIC=-1873.05\n"
]
}
],
"source": [
"print(mdl_4_2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nuYCITvEcSQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::tsdisplay(mdl_4_2$residuals)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"lag = 2 p-value = 0.233\"\n",
"[1] \"lag = 3 p-value = 0.48918\"\n",
"[1] \"lag = 4 p-value = 0.60088\"\n",
"[1] \"lag = 5 p-value = 0.15918\"\n",
"[1] \"lag = 6 p-value = 0.12887\"\n",
"[1] \"lag = 7 p-value = 0.13701\"\n",
"[1] \"lag = 8 p-value = 0.1124\"\n",
"[1] \"lag = 9 p-value = 0.16249\"\n",
"[1] \"lag = 10 p-value = 0.21714\"\n",
"[1] \"lag = 11 p-value = 0.28468\"\n",
"[1] \"lag = 12 p-value = 0.32625\"\n",
"[1] \"lag = 13 p-value = 0.40394\"\n",
"[1] \"lag = 14 p-value = 0.16598\"\n",
"[1] \"lag = 15 p-value = 0.21319\"\n",
"[1] \"lag = 16 p-value = 0.2484\"\n",
"[1] \"lag = 17 p-value = 0.28167\"\n",
"[1] \"lag = 18 p-value = 0.24748\"\n",
"[1] \"lag = 19 p-value = 0.1376\"\n",
"[1] \"lag = 20 p-value = 0.1608\"\n"
]
}
],
"source": [
"for(i in (length(coef(mdl_4_2)) + 1):20){\n",
" aa <- Box.test(mdl_4_2$residuals, lag = i, type = \"Ljung-Box\", fitdf = length(coef(mdl_4_2)))\n",
" print(paste0(\"lag = \", i, \" p-value = \", round(aa$p.value, 5)))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residuals are white noise. So this model appears to be adequate. The residuals of the previous model:"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"lag = 7 p-value = 0.06977\"\n",
"[1] \"lag = 8 p-value = 0.06436\"\n",
"[1] \"lag = 9 p-value = 0.13757\"\n",
"[1] \"lag = 10 p-value = 0.21511\"\n",
"[1] \"lag = 11 p-value = 0.32666\"\n",
"[1] \"lag = 12 p-value = 0.38641\"\n",
"[1] \"lag = 13 p-value = 0.49784\"\n",
"[1] \"lag = 14 p-value = 0.22004\"\n",
"[1] \"lag = 15 p-value = 0.29774\"\n",
"[1] \"lag = 16 p-value = 0.35561\"\n",
"[1] \"lag = 17 p-value = 0.3971\"\n",
"[1] \"lag = 18 p-value = 0.36719\"\n",
"[1] \"lag = 19 p-value = 0.23814\"\n",
"[1] \"lag = 20 p-value = 0.28593\"\n"
]
}
],
"source": [
"for(i in (length(coef(mdl_4_1))+1):20){\n",
" aa <- Box.test(mdl_4_1$residuals, lag = i, type = \"Ljung-Box\", fitdf = length(coef(mdl_4_1)))\n",
" print(paste0(\"lag = \", i, \" p-value = \", round(aa$p.value, 5)))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"are also WN."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## - `auto.arima` without any restrictions"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [],
"source": [
"mdl_4_3 <- forecast::auto.arima(lnyse)"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Series: lnyse \n",
"ARIMA(0,1,0) with drift \n",
"\n",
"Coefficients:\n",
" drift\n",
" 0.0069\n",
"s.e. 0.0018\n",
"\n",
"sigma^2 estimated as 0.00165: log likelihood=942.79\n",
"AIC=-1881.59 AICc=-1881.56 BIC=-1873.05\n"
]
}
],
"source": [
"print(mdl_4_3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, `mdl_4_3` is the same as `mdl_4_2`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we'd like, we can compare the models via AIC/BIC:"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" mdl_4_1 mdl_4_2\n",
"AIC -1877.962 -1881.587\n",
"BIC -1848.078 -1873.049\n"
]
}
],
"source": [
"a <- data.frame(mdl_4_1 = c(AIC(mdl_4_1), BIC(mdl_4_1)),\n",
" mdl_4_2 = c(AIC(mdl_4_2), BIC(mdl_4_2)))\n",
"rownames(a) <- c(\"AIC\", \"BIC\")\n",
"print(a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Overall, the second model, `mdl_4_2`, appears to be better, since its AIC and BIC values are smaller."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"Intuitively, we may assume that we can simply differenciate the data and then fit the model on the differences."
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 5)\n",
"options(repr.plot.height = 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For, example, the $\\rm ARIMA(0, 1, 0)$ on $Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"ARIMA(0,1,0) with drift \n",
"\n",
"Coefficients:\n",
" drift\n",
" 0.0069\n",
"s.e. 0.0018\n",
"\n",
"sigma^2 estimated as 0.00165: log likelihood=942.79\n",
"AIC=-1881.59 AICc=-1881.56 BIC=-1873.05"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m_tst_1 <- forecast::Arima(lnyse, order = c(0, 1, 0), include.drift = TRUE)\n",
"m_tst_1"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAHgCAMAAABOyeNrAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nLJCAWCABsUACYoEExAIJiAUS/gPCLGkTD7mLFQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(lnyse)\n",
"lines(m_tst_1$fitted, col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Can be written as a $\\rm ARIMA(0, 0, 0)$ model on the differences $\\Delta Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: diff(lnyse) \n",
"ARIMA(0,0,0) with non-zero mean \n",
"\n",
"Coefficients:\n",
" mean\n",
" 0.0069\n",
"s.e. 0.0018\n",
"\n",
"sigma^2 estimated as 0.00165: log likelihood=942.79\n",
"AIC=-1881.59 AICc=-1881.56 BIC=-1873.05"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"m_tst_2 <- forecast::Arima(diff(lnyse), order = c(0, 0, 0), include.constant = TRUE)\n",
"m_tst_2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While the model **appears** to be the same. If we were to estimate the fit - the fitted values are then calculated for $\\widehat{\\Delta Y_t}$:"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Feb Mar Apr May Jun Jul\n",
"1952 0.00686458 0.00686458 0.00686458 0.00686458 0.00686458 0.00686458\n",
" Aug Sep Oct Nov\n",
"1952 0.00686458 0.00686458 0.00686458 0.00686458"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(fitted(m_tst_2), 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which are constant. This is to be expected, since our model for $\\widehat{\\Delta Y_t}$ is in fact a constant. Unfortunately, in this case the forecasts are **NOT** the same the $\\rm ARIMA(0, 1, 0)$ models on $Y_t$, even if we compare the differences:"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 15)\n",
"options(repr.plot.height = 4)"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nrkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(diff(lnyse), lwd = 2)\n",
"lines(fitted(m_tst_2), col = \"red\")\n",
"lines(diff(m_tst_1$fitted), col = \"blue\", lty = 2)\n",
"legend(\"bottomleft\", y.intersp = 3, cex = 0.8,\n",
" legend = c(as.expression(bquote(Delta~Y[t])), as.expression(bquote(widehat(Delta~Y)[t])), as.expression(bquote(widehat(Y)[t] - Y[t-1]))),\n",
" lty = c(1, 1, 2), col = c(\"black\", \"red\", \"blue\"), lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check out a comment on [stackoverflow](https://stats.stackexchange.com/a/32799) by the author of the forecast package. For $\\Delta Y_t \\sim AR(1)$ the difference is that:\n",
"\n",
"- When fitting a $I(1)$ model on $Y_t$, the fitted values are: $$\\widehat{Y}_t = Y_{t-1} + \\widehat{\\gamma}\\cdot(Y_{t-1} - Y_{t-2})$$\n",
"\n",
"- When fitting a $I(0)$ model on $\\Delta Y_t$, the fitted values are: $$\\widehat{\\Delta {Y}}_t = \\widehat{\\gamma}\\cdot(Y_{t-1} - Y_{t-2})$$\n",
"\n",
"In our case this is equivalent to comparing the fitted values of $\\widehat{(Y_{t-1} - Y_{t-2})} = \\widehat{\\alpha}$ versus $\\widehat{Y}_t = \\widehat{\\alpha} + Y_{t-1}$.\n",
"\n",
"The problem is that in general $\\widehat{Y}_t - Y_{t-1} \\neq \\widehat{\\Delta {Y}}_t$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fortunately, once we have the coefficient estimates we can use the parametrization (assuming that $H_0: \\rho = 0$ is not rejected): $\\Delta Y_t = \\alpha + \\delta \\cdot t \\sum_{j = 1}^{p-1} \\gamma_j \\Delta Y_{t-j} + \\epsilon_t$\n",
"\n",
"In this case, our equation is: $\\Delta Y_t = \\alpha + \\epsilon_t$.\n",
"\n",
"Since we do not want to calulate $\\widehat{\\Delta Y}_t$, but rather $\\widehat{Y}_t$, we simply apply the definition of $\\Delta$ and get: $Y_t = \\alpha + Y_{t-1} + \\epsilon_t$.\n",
"\n",
"**The two equations are equivalent, just with a different parametrization. If we fit a model on manually-calculated $\\Delta Y_t$ - there is no way for the software to detect that you took the differences MANUALLY**. \n",
"\n",
"This is also evident from the fact that the coefficients are identical (though they may sometimes differ due to different starting values for differenced versus non-differenced data).\n",
"\n",
"Remember that **the fitted values are calculated as a conditional expectation on $Y_t$, conditionally that any variables on the right-hand-side are given**, hence (replacing $\\epsilon_t$ with its mean of zero):\n",
"$$\n",
"\\widehat{Y}_t = \\widehat{\\alpha} + Y_{t-1},\\ t = 2,...,T\n",
"$$\n",
"Assuming that our series starts at $Y_1$ with $Y_s = 0$ for $s \\leq 0$.\n",
"\n",
"(if we had a moving-average part, we could calculate $\\widehat{\\epsilon}_s = Y_s - \\widehat{Y}_s$ for $s < t$ and use the residuals for for $t + 1$).\n",
"\n",
"In the case of the differences model, we have that:"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {},
"outputs": [],
"source": [
"y_fit <- coef(m_tst_2) + lnyse[-length(lnyse)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first fitted value is equal to the true value"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"4.60517018599809"
],
"text/latex": [
"4.60517018599809"
],
"text/markdown": [
"4.60517018599809"
],
"text/plain": [
"[1] 4.60517"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lnyse[1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compare the fitted values with the ones from the ARIMA model on $Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"Y_ARIMA | dY_ARMA | diff |
\n",
"\n",
"\t4.600572 | NA | NA |
\n",
"\t4.612035 | 4.612035 | -2.486900e-14 |
\n",
"\t4.627495 | 4.627495 | 1.154632e-14 |
\n",
"\t4.595446 | 4.595446 | 1.154632e-14 |
\n",
"\t4.636687 | 4.636687 | 1.154632e-14 |
\n",
"\t4.586286 | 4.586286 | 1.154632e-14 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" Y\\_ARIMA & dY\\_ARMA & diff\\\\\n",
"\\hline\n",
"\t 4.600572 & NA & NA\\\\\n",
"\t 4.612035 & 4.612035 & -2.486900e-14\\\\\n",
"\t 4.627495 & 4.627495 & 1.154632e-14\\\\\n",
"\t 4.595446 & 4.595446 & 1.154632e-14\\\\\n",
"\t 4.636687 & 4.636687 & 1.154632e-14\\\\\n",
"\t 4.586286 & 4.586286 & 1.154632e-14\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"Y_ARIMA | dY_ARMA | diff | \n",
"|---|---|---|---|---|---|\n",
"| 4.600572 | NA | NA | \n",
"| 4.612035 | 4.612035 | -2.486900e-14 | \n",
"| 4.627495 | 4.627495 | 1.154632e-14 | \n",
"| 4.595446 | 4.595446 | 1.154632e-14 | \n",
"| 4.636687 | 4.636687 | 1.154632e-14 | \n",
"| 4.586286 | 4.586286 | 1.154632e-14 | \n",
"\n",
"\n"
],
"text/plain": [
" Y_ARIMA dY_ARMA diff \n",
"1 4.600572 NA NA\n",
"2 4.612035 4.612035 -2.486900e-14\n",
"3 4.627495 4.627495 1.154632e-14\n",
"4 4.595446 4.595446 1.154632e-14\n",
"5 4.636687 4.636687 1.154632e-14\n",
"6 4.586286 4.586286 1.154632e-14"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"aa <- data.frame(m_tst_1$fitted, c(NA, y_fit))\n",
"colnames(aa) <- c(\"Y_ARIMA\", \"dY_ARMA\")\n",
"aa$diff <- aa$Y_ARIMA - aa$dY_ARMA\n",
"head(aa)"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Min. 1st Qu. Median Mean 3rd Qu. Max. NA's \n",
" 0 0 0 0 0 0 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(aa$diff)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Obviously then `diff(aa$Y_ARIMA)` and `diff(aa$dY_ARMA)` will also be equal. However, this is different from `fitted(m_tst_2)`:"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"Y_ARIMA_diff | dY_ARMA_diff | diff |
\n",
"\n",
"\t 0.01146288 | 0.00686458 | 0.004598303 |
\n",
"\t 0.01546000 | 0.00686458 | 0.008595420 |
\n",
"\t-0.03204900 | 0.00686458 | -0.038913580 |
\n",
"\t 0.04124100 | 0.00686458 | 0.034376420 |
\n",
"\t-0.05040100 | 0.00686458 | -0.057265580 |
\n",
"\t 0.02504100 | 0.00686458 | 0.018176420 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" Y\\_ARIMA\\_diff & dY\\_ARMA\\_diff & diff\\\\\n",
"\\hline\n",
"\t 0.01146288 & 0.00686458 & 0.004598303\\\\\n",
"\t 0.01546000 & 0.00686458 & 0.008595420\\\\\n",
"\t -0.03204900 & 0.00686458 & -0.038913580\\\\\n",
"\t 0.04124100 & 0.00686458 & 0.034376420\\\\\n",
"\t -0.05040100 & 0.00686458 & -0.057265580\\\\\n",
"\t 0.02504100 & 0.00686458 & 0.018176420\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"Y_ARIMA_diff | dY_ARMA_diff | diff | \n",
"|---|---|---|---|---|---|\n",
"| 0.01146288 | 0.00686458 | 0.004598303 | \n",
"| 0.01546000 | 0.00686458 | 0.008595420 | \n",
"| -0.03204900 | 0.00686458 | -0.038913580 | \n",
"| 0.04124100 | 0.00686458 | 0.034376420 | \n",
"| -0.05040100 | 0.00686458 | -0.057265580 | \n",
"| 0.02504100 | 0.00686458 | 0.018176420 | \n",
"\n",
"\n"
],
"text/plain": [
" Y_ARIMA_diff dY_ARMA_diff diff \n",
"1 0.01146288 0.00686458 0.004598303\n",
"2 0.01546000 0.00686458 0.008595420\n",
"3 -0.03204900 0.00686458 -0.038913580\n",
"4 0.04124100 0.00686458 0.034376420\n",
"5 -0.05040100 0.00686458 -0.057265580\n",
"6 0.02504100 0.00686458 0.018176420"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bbb <- data.frame(diff(m_tst_1$fitted), m_tst_2$fitted)\n",
"colnames(bbb) <- c(\"Y_ARIMA_diff\", \"dY_ARMA_diff\")\n",
"bbb$diff <- bbb$Y_ARIMA - bbb$dY_ARMA\n",
"head(bbb)"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Min. 1st Qu. Median Mean 3rd Qu. Max. \n",
"-0.2253176 -0.0242888 0.0024959 -0.0000115 0.0260387 0.1579624 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(bbb$diff)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All in all, it is much easier to specify the model for $Y_t$, instead of manually calculating the differences and estimating a model on $\\Delta Y_t$, as most forecasting and fittign functions are readily available.\n",
"\n",
"## **[INFO: END]**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# (5) Writing down the model for $\\Delta Y_t$ and $Y_t$\n",
"\n",
"Assume that we have selected the following model as the \"best\" one:"
]
},
{
"cell_type": "code",
"execution_count": 131,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"ARIMA(0,1,0) with drift \n",
"\n",
"Coefficients:\n",
" drift\n",
" 0.0069\n",
"s.e. 0.0018\n",
"\n",
"sigma^2 estimated as 0.00165: log likelihood=942.79\n",
"AIC=-1881.59 AICc=-1881.56 BIC=-1873.05"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_4_2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which we can write as: $\\Delta Y_{t} = 0.0069 + \\epsilon_t$, or equivalently as: $Y_t = 0.0069 + Y_{t-1} + \\epsilon_t$. In other words, this is a random walk with drift."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assume that we are not so \"lucky\" and our model is much more complex. For example"
]
},
{
"cell_type": "code",
"execution_count": 132,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) -0.07357 0.27887 -0.26382 0.79203\n",
"L(d(lnyse), 1:5)1 0.04398 0.04382 1.00357 0.31606\n",
"L(d(lnyse), 1:5)2 -0.03932 0.04380 -0.89786 0.36968\n",
"L(d(lnyse), 1:5)3 0.01035 0.04380 0.23620 0.81337\n",
"L(d(lnyse), 1:5)4 0.02288 0.04376 0.52299 0.60121\n",
"L(d(lnyse), 1:5)5 0.09225 0.04373 2.10951 0.03538\n",
"time(lnyse) 0.00004 0.00014 0.28548 0.77539\n"
]
}
],
"source": [
"mod.2 <- dynlm(d(lnyse) ~ L(d(lnyse), 1:5) + time(lnyse))\n",
"print(round(coef(summary(mod.2)), 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we needed the trend for unit root testing - having removed the insignificant $\\rho$ coefficient, we could try to remove the insignificant trend and improve our model. But we will assume that this model is acceptible as is."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remembering the model parametrization of `dynlm`, the estimated model for $\\Delta Y_t$ is: \n",
"\n",
"$\\Delta Y_t = -0.07357 + 0.00004 \\cdot t + 0.04398 \\Delta Y_{t-1} -0.03932 \\Delta Y_{t-2} + 0.01035 \\Delta Y_{t-3} + 0.02288 \\Delta Y_{t-4} + 0.09225 \\Delta Y_{t-5} + \\epsilon_t$, \n",
"\n",
"which we can re-write as a model for $Y_t$. \n",
"\n",
"We use the property $\\gamma_j = -[\\phi_{j+1} + ... + \\phi_p]$, $j = 1, ..., p - 1$ and the expression of $\\rho$ to get the coefficients:\n",
"\n",
"$\n",
"\\begin{aligned}\n",
"\\gamma_5 &= - \\phi_6 &&\\Longrightarrow \\phi_6 = - \\gamma_5 = -0.09225\\\\\n",
"\\gamma_4 &= - [\\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_5 = - \\gamma_4 - \\phi_6 = -0.02288+0.09225 = 0.06937\\\\\n",
"\\gamma_3 &= - [\\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_4 = - \\gamma_3 - [\\phi_5 + \\phi_6] = - \\gamma_3 + \\gamma_4 = -0.01035+0.02288 = 0.01253\\\\\n",
"\\gamma_2 &= - [\\phi_3 + \\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_3 = - \\gamma_2 + \\gamma_3 = 0.03932 + 0.01035 = 0.04967\\\\\n",
"\\gamma_1 &= - [\\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6] &&\\Longrightarrow \\phi_2 = - \\gamma_1 + \\gamma_2 = -0.04398 -0.03932 = -0.0833\\\\\n",
"\\rho &= \\phi_1 + \\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6 - 1,\\text{ since } \\rho = 0 &&\\Longrightarrow \\phi_1 = 1 - (\\phi_2 + \\phi_3 + \\phi_4 + \\phi_5 + \\phi_6) = 1 + \\gamma_1= 1 + 0.04398 = 1.04398\n",
"\\end{aligned}\n",
"$\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, the equivalent model for $Y_t$ is:\n",
"\n",
"$Y_t = -0.07357 + 0.00004 \\cdot t + 1.04398 Y_{t-1} -0.0833 Y_{t-2} + 0.04967 Y_{t-3} + 0.01253 Y_{t-4} + 0.06937 Y_{t-5} -0.09225 Y_{t-6} + \\epsilon_t$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"To verify that this is indeed the correct transformation, we can try to simulate a few observations with the same residuals:"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"N <- 200\n",
"eps <- rnorm(mean = 0, sd = 1, n = N)\n",
"tt <- 1:length(eps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we will simulate $Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {},
"outputs": [],
"source": [
"Y <- NULL\n",
"Y[1] <- -0.07357 + 0.00004 * tt[1] + eps[1]\n",
"Y[2] <- -0.07357 + 0.00004 * tt[2] + 1.04398 * Y[1] + eps[2]\n",
"Y[3] <- -0.07357 + 0.00004 * tt[3] + 1.04398 * Y[2] −0.0833 * Y[1] + eps[3]\n",
"Y[4] <- -0.07357 + 0.00004 * tt[4] + 1.04398 * Y[3] −0.0833 * Y[2] + 0.04967 * Y[1] + eps[4]\n",
"Y[5] <- -0.07357 + 0.00004 * tt[5] + 1.04398 * Y[4] −0.0833 * Y[3] + 0.04967 * Y[2] + 0.01253 * Y[1] + eps[5]\n",
"Y[6] <- -0.07357 + 0.00004 * tt[6] + 1.04398 * Y[5] −0.0833 * Y[4] + 0.04967 * Y[3] + 0.01253 * Y[2] + 0.06937 * Y[1] + eps[6]\n",
"for(j in 7:N){\n",
" Y[j] <- -0.07357 + 0.00004 * tt[j] + 1.04398 * Y[j-1] −0.0833 * Y[j-2] + 0.04967 * Y[j - 3] + 0.01253 * Y[j - 4] + 0.06937 * Y[j - 5] − 0.09225 * Y[j - 6] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Secondly, we will simulate $\\Delta Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"outputs": [],
"source": [
"dY <- NULL\n",
"dY[1] <- -0.0735 + 0.00004 * tt[1] + eps[1]\n",
"dY[2] <- -0.07357 + 0.00004 * tt[2] + 0.04398 * dY[1] + eps[2]\n",
"dY[3] <- -0.07357 + 0.00004 * tt[3] + 0.04398 * dY[2] −0.03932 * dY[1] + eps[3]\n",
"dY[4] <- -0.07357 + 0.00004 * tt[4] + 0.04398 * dY[3] −0.03932 * dY[2] + 0.01035 * dY[1] + eps[4]\n",
"dY[5] <- -0.07357 + 0.00004 * tt[5] + 0.04398 * dY[4] −0.03932 * dY[3] + 0.01035 * dY[2] + 0.02288 * dY[1] + eps[5]\n",
"for(j in 6:N){\n",
" dY[j] <- -0.07357 + 0.00004 * tt[j] + 0.04398 * dY[j-1] −0.03932 * dY[j-2] + 0.01035 * dY[j - 3] + 0.02288 * dY[j - 4] + 0.09225 * dY[j - 5] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we will assume that the first `100`, or so, observations of $Y_t$ are burn-in values (since the first couple of values assume that $Y_j = \\epsilon_j = 0$, for $j \\leq 0$). This means that we treat treat the first `101` $\\Delta Y_t$ values as burn-in values as well and drop them:"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {},
"outputs": [],
"source": [
"Y <- Y[-c(1:100)]"
]
},
{
"cell_type": "code",
"execution_count": 137,
"metadata": {},
"outputs": [],
"source": [
"dY <- dY[-c(1:101)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compare $\\Delta Y_t$ with $Y_t - Y_{t-1}$:"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"diff.Y. | dY | DIFFERENCE |
\n",
"\n",
"\t 0.4191779 | 0.4191779 | 0 |
\n",
"\t-0.1389262 | -0.1389262 | 0 |
\n",
"\t-0.5043527 | -0.5043527 | 0 |
\n",
"\t-1.1470432 | -1.1470432 | 0 |
\n",
"\t-0.2097488 | -0.2097488 | 0 |
\n",
"\t-0.7880470 | -0.7880470 | 0 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" diff.Y. & dY & DIFFERENCE\\\\\n",
"\\hline\n",
"\t 0.4191779 & 0.4191779 & 0 \\\\\n",
"\t -0.1389262 & -0.1389262 & 0 \\\\\n",
"\t -0.5043527 & -0.5043527 & 0 \\\\\n",
"\t -1.1470432 & -1.1470432 & 0 \\\\\n",
"\t -0.2097488 & -0.2097488 & 0 \\\\\n",
"\t -0.7880470 & -0.7880470 & 0 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"diff.Y. | dY | DIFFERENCE | \n",
"|---|---|---|---|---|---|\n",
"| 0.4191779 | 0.4191779 | 0 | \n",
"| -0.1389262 | -0.1389262 | 0 | \n",
"| -0.5043527 | -0.5043527 | 0 | \n",
"| -1.1470432 | -1.1470432 | 0 | \n",
"| -0.2097488 | -0.2097488 | 0 | \n",
"| -0.7880470 | -0.7880470 | 0 | \n",
"\n",
"\n"
],
"text/plain": [
" diff.Y. dY DIFFERENCE\n",
"1 0.4191779 0.4191779 0 \n",
"2 -0.1389262 -0.1389262 0 \n",
"3 -0.5043527 -0.5043527 0 \n",
"4 -1.1470432 -1.1470432 0 \n",
"5 -0.2097488 -0.2097488 0 \n",
"6 -0.7880470 -0.7880470 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dt_compare <- data.frame(diff(Y), dY)\n",
"dt_compare$DIFFERENCE <- round(diff(Y) - dY, 10)\n",
"head(dt_compare)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that there is no difference between the simulate $Y_t - Y_{t-1}$ (`diff.Y.`), which was calculated from the simulated $Y_t$ series, and $\\Delta Y_t$ (`dY`).\n",
"\n",
"We can also visually compare the charts:"
]
},
{
"cell_type": "code",
"execution_count": 139,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nmkYQAgCaRhACAJpGEAIAmvY/AYczfgBJUNUAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(ts(diff(Y)), col = \"red\", lwd = 2)\n",
"lines(ts(dY), col = \"blue\", lty = 2, lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, the two models are equivalent. For simulation and forecasting we may be more interested in $Y_t$ model, as it is the original series, which we are interested in.\n",
"\n",
"\n",
"## **[INFO: END]**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the other hand, if our model was specified via `Arima`, we would need to differently specify the model."
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"Regression with ARIMA(5,1,0) errors \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 tt\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::Arima(lnyse, order = c(5, 1, 0), xreg = data.frame(tt = 1:length(lnyse)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which is equivalent to:"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"ARIMA(5,1,0) with drift \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 drift\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::Arima(lnyse, order = c(5, 1, 0), include.drift = TRUE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"or"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"arima(x = lnyse, order = c(5, 1, 0), xreg = 1:length(lnyse))\n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 1:length(lnyse)\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001627: log likelihood = 945.98, aic = -1877.96"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"arima(lnyse, order = c(5, 1, 0), xreg = 1:length(lnyse))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This model, estimated via `Arima` for $\\Delta Y_t$ is: \n",
"\n",
"$\n",
"\\begin{cases}\n",
"\\Delta Y_t &= \\tilde{\\delta} + u_t \\\\\n",
"u_t &= \\gamma_1 u_{t-1} + \\gamma_2 u_{t-2} + \\gamma_3 u_{t-3} + \\gamma_4 u_{t-4} + \\gamma_5 u_{t-5} + \\epsilon_t\n",
"\\end{cases}\n",
"$\n",
"\n",
"which is equivalent to:\n",
"\n",
"$\n",
"\\Delta Y_t = \\tilde{\\delta} (1 - \\gamma_1 - \\gamma_2 - \\gamma_3 - \\gamma_4 - \\gamma_5) + \\gamma_1 \\Delta Y_{t-1} + \\gamma_2 \\Delta Y_{t-2} + \\gamma_3 \\Delta Y_{t-3} + \\gamma_4 \\Delta Y_{t-4} + \\gamma_5 \\Delta Y_{t-5} + \\epsilon_t\n",
"$\n",
"\n",
"an important distinction is **how** we arrived at such a model. In the previous case - we have transformed $Y_t$ into an equivalent model via differences in order to test whether a unit root exists. Since it did - we removed an additional insignificant parameter and were left with a model, which included both a constant and a trend in the differences model.\n",
"\n",
"Assuming that the parametrization is the same as before, with $\\rho = 0$ - we arrive at the following coefficient parametrizations:\n",
"\n",
"- $\\tilde{\\delta} (1 - \\gamma_1 - \\gamma_2 - \\gamma_3 - \\gamma_4 - \\gamma_5)$ is the constant.\n",
"- The remaining coefficient have the same expressions as before:
\n",
"$\n",
"\\begin{aligned}\n",
"\\phi_1 &= 1 + \\gamma_1 \\\\\n",
"\\phi_2 &= -\\gamma_1 + \\gamma_2\\\\\n",
"\\phi_3 &= -\\gamma_2 + \\gamma_3\\\\\n",
"\\phi_4 &= -\\gamma_3 + \\gamma_4\\\\\n",
"\\phi_5 &= -\\gamma_4 + \\gamma_5\\\\\n",
"\\phi_6 &= -\\gamma_5\n",
"\\end{aligned}\n",
"$\n",
"\n",
"So the final equation is\n",
"$$\n",
"\\begin{aligned}\n",
"Y_t &= \\tilde{\\delta} (1 - \\gamma_1 - \\gamma_2 - \\gamma_3 - \\gamma_4 - \\gamma_5) + (1 + \\gamma_1) Y_{t-1} + (\\gamma_2-\\gamma_1) Y_{t-2} + (\\gamma_3 - \\gamma_2) Y_{t-3} + (\\gamma_4-\\gamma_3) Y_{t-4} + (\\gamma_5-\\gamma_4) Y_{t-5} + (-\\gamma_5)Y_{t-6} + \\epsilon_t\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will skip inputting the coefficient values into the equation as we have already done so in the previous example.\n",
"\n",
"We **will** however, show a simulation example to highlight that the two equations produce the same processes.\n",
"\n",
"Once again, our model for $\\Delta Y_t$ is:"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"ARIMA(5,1,0) with drift \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 drift\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::Arima(lnyse, order = c(5, 1, 0), include.drift = TRUE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"To again verify the equivalency between the models, we will simulate $Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {},
"outputs": [],
"source": [
"set.seed(123)\n",
"N <- 200\n",
"eps <- rnorm(mean = 0, sd = 1, n = N)\n",
"tt <- 1:length(eps)"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.0060237"
],
"text/latex": [
"0.0060237"
],
"text/markdown": [
"0.0060237"
],
"text/plain": [
"[1] 0.0060237"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"delta_coef <- 0.0069 * (1 - 0.0380 + 0.0350 - 0.0089 - 0.0228 - 0.0923)\n",
"delta_coef"
]
},
{
"cell_type": "code",
"execution_count": 146,
"metadata": {},
"outputs": [],
"source": [
"Y <- NULL\n",
"Y[1] <- delta_coef + eps[1]\n",
"Y[2] <- delta_coef + (1 + 0.0380) * Y[1] + eps[2]\n",
"Y[3] <- delta_coef + (1 + 0.0380) * Y[2] + (-0.0350 - 0.0380) * Y[1] + eps[3]\n",
"Y[4] <- delta_coef + (1 + 0.0380) * Y[3] + (-0.0350 - 0.0380) * Y[2] + (0.0089 + 0.0350) * Y[1] + eps[4]\n",
"Y[5] <- delta_coef + (1 + 0.0380) * Y[4] + (-0.0350 - 0.0380) * Y[3] + (0.0089 + 0.0350) * Y[2] + (0.0228 - 0.0089) * Y[1] + eps[5]\n",
"Y[6] <- delta_coef + (1 + 0.0380) * Y[5] + (-0.0350 - 0.0380) * Y[4] + (0.0089 + 0.0350) * Y[3] + (0.0228 - 0.0089) * Y[2] + (0.0923 - 0.0228) * Y[1] + eps[6]\n",
"for(j in 7:N){\n",
" Y[j] <- delta_coef + (1 + 0.0380) * Y[j-1] + (-0.0350 - 0.0380) * Y[j-2] + (0.0089 + 0.0350) * Y[j - 3] + (0.0228 - 0.0089) * Y[j - 4] + (0.0923 - 0.0228) * Y[j - 5] − 0.0923 * Y[j - 6] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Secondly, we will simulate $\\Delta Y_t$:"
]
},
{
"cell_type": "code",
"execution_count": 147,
"metadata": {},
"outputs": [],
"source": [
"dY <- NULL\n",
"dY[1] <- delta_coef + eps[1]\n",
"dY[2] <- delta_coef + 0.0380 * dY[1] + eps[2]\n",
"dY[3] <- delta_coef + 0.0380 * dY[2] -0.0350 * dY[1] + eps[3]\n",
"dY[4] <- delta_coef + 0.0380 * dY[3] -0.0350 * dY[2] + 0.0089 * dY[1] + eps[4]\n",
"dY[5] <- delta_coef + 0.0380 * dY[4] -0.0350 * dY[3] + 0.0089 * dY[2] + 0.0228 * dY[1] + eps[5]\n",
"for(j in 6:N){\n",
" dY[j] <- delta_coef + 0.0380 * dY[j-1] -0.0350 * dY[j-2] + 0.0089 * dY[j - 3] + 0.0228 * dY[j - 4] + 0.0923 * dY[j - 5] + eps[j] \n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we will assume that the first `100`, or so, observations of $Y_t$ are burn-in values (since the first couple of values assume that $Y_j = \\epsilon_j = 0$, for $j \\leq 0$). This means that we treat treat the first `101` $\\Delta Y_t$ values as burn-in values as well and drop them:"
]
},
{
"cell_type": "code",
"execution_count": 148,
"metadata": {},
"outputs": [],
"source": [
"Y <- Y[-c(1:100)]"
]
},
{
"cell_type": "code",
"execution_count": 149,
"metadata": {},
"outputs": [],
"source": [
"dY <- dY[-c(1:101)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compare $\\Delta Y_t$ with $Y_t - Y_{t-1}$:"
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"diff.Y. | dY | DIFFERENCE |
\n",
"\n",
"\t 0.5067329 | 0.5067329 | 0 |
\n",
"\t-0.0581769 | -0.0581769 | 0 |
\n",
"\t-0.4142284 | -0.4142284 | 0 |
\n",
"\t-1.0578262 | -1.0578262 | 0 |
\n",
"\t-0.1185169 | -0.1185169 | 0 |
\n",
"\t-0.7046021 | -0.7046021 | 0 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" diff.Y. & dY & DIFFERENCE\\\\\n",
"\\hline\n",
"\t 0.5067329 & 0.5067329 & 0 \\\\\n",
"\t -0.0581769 & -0.0581769 & 0 \\\\\n",
"\t -0.4142284 & -0.4142284 & 0 \\\\\n",
"\t -1.0578262 & -1.0578262 & 0 \\\\\n",
"\t -0.1185169 & -0.1185169 & 0 \\\\\n",
"\t -0.7046021 & -0.7046021 & 0 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"diff.Y. | dY | DIFFERENCE | \n",
"|---|---|---|---|---|---|\n",
"| 0.5067329 | 0.5067329 | 0 | \n",
"| -0.0581769 | -0.0581769 | 0 | \n",
"| -0.4142284 | -0.4142284 | 0 | \n",
"| -1.0578262 | -1.0578262 | 0 | \n",
"| -0.1185169 | -0.1185169 | 0 | \n",
"| -0.7046021 | -0.7046021 | 0 | \n",
"\n",
"\n"
],
"text/plain": [
" diff.Y. dY DIFFERENCE\n",
"1 0.5067329 0.5067329 0 \n",
"2 -0.0581769 -0.0581769 0 \n",
"3 -0.4142284 -0.4142284 0 \n",
"4 -1.0578262 -1.0578262 0 \n",
"5 -0.1185169 -0.1185169 0 \n",
"6 -0.7046021 -0.7046021 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dt_compare <- data.frame(diff(Y), dY)\n",
"dt_compare$DIFFERENCE <- round(diff(Y) - dY, 10)\n",
"head(dt_compare)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that there is no difference between the simulate $Y_t - Y_{t-1}$ (`diff.Y.`), which was calculated from the simulated $Y_t$ series, and $\\Delta Y_t$ (`dY`).\n",
"\n",
"We can also visually compare the charts:"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABwgAAAHgCAMAAACGislhAAAANlBMVEUAAAAAAP9NTU1oaGh8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\n9zLT1br1XwAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(ts(diff(Y)), col = \"red\", lwd = 2)\n",
"lines(ts(dY), col = \"blue\", lty = 2, lwd = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **[INFO: END]**\n",
"\n",
"----\n",
"----\n",
"----\n",
"\n",
"# (6) Calculate the \\(10\\)-step ahead forecasts for the original series."
]
},
{
"cell_type": "code",
"execution_count": 152,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 10)\n",
"options(repr.plot.height = 4)"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [],
"source": [
"tt_forc <- data.frame(tt = length(lnyse) + 1:10)"
]
},
{
"cell_type": "code",
"execution_count": 154,
"metadata": {},
"outputs": [],
"source": [
"mdl_4_1_forc <- forecast(mdl_4_1, h = 10, xreg = tt_forc)\n",
"mdl_4_2_forc <- forecast(mdl_4_2, h = 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will plot the original historical data, the fitted values and the forecasts."
]
},
{
"cell_type": "code",
"execution_count": 155,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(exp(lnyse),\n",
" xlim = c(floor(min(time(lnyse))), floor(max(time(lnyse))) + 1), \n",
" ylim = c(0, max(exp(mdl_4_1_forc$mean), exp(mdl_4_2_forc$mean))))\n",
"#\n",
"lines(exp(fitted(mdl_4_1)), col = \"red\", lty = 2)\n",
"lines(exp(fitted(mdl_4_2)), col = \"blue\", lty = 2)\n",
"#\n",
"lines(exp(mdl_4_1_forc$mean), col = \"red\", lty = 2)\n",
"lines(exp(mdl_4_2_forc$mean), col = \"blue\", lty = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" As it is difficult to see, we will also reduce the time window to see the last few years"
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAHgCAMAAACCSWStAAAANlBMVEUAAAAAAP9NTU1oaGh8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\nYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot.ts(window(exp(lnyse), start = 1990), \n",
" xlim = c(1990, floor(max(time(lnyse))) + 1), \n",
" ylim = c(1800, max(exp(mdl_4_1_forc$mean), exp(mdl_4_2_forc$mean))), \n",
" lwd = 2)\n",
"#\n",
"lines(exp(fitted(mdl_4_1)), col = \"red\", lty = 2)\n",
"lines(exp(fitted(mdl_4_2)), col = \"blue\", lty = 2)\n",
"#\n",
"lines(exp(mdl_4_1_forc$mean), col = \"red\", lty = 2)\n",
"lines(exp(mdl_4_2_forc$mean), col = \"blue\", lty = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the model forecasts do not appear to differ by a whole lot."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"\n",
"# (7) Model Cross-validation\n",
"\n",
"Assume that our best model (again, we can select it via AIC or BIC but we choose a more complex one for a more general example) is:"
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"Regression with ARIMA(5,1,0) errors \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 tt\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_4_1"
]
},
{
"cell_type": "code",
"execution_count": 158,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: lnyse \n",
"ARIMA(5,1,0) with drift \n",
"\n",
"Coefficients:\n",
" ar1 ar2 ar3 ar4 ar5 drift\n",
" 0.0380 -0.0350 0.0089 0.0228 0.0923 0.0069\n",
"s.e. 0.0433 0.0434 0.0434 0.0434 0.0434 0.0020\n",
"\n",
"sigma^2 estimated as 0.001645: log likelihood=945.98\n",
"AIC=-1877.96 AICc=-1877.75 BIC=-1848.08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"forecast::Arima(lnyse, order = c(5, 1, 0), include.drift = TRUE)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, we will use $k$ of around $20\\%$ of our series and create $k = \\lfloor 0.2 \\cdot T \\rfloor$ samples and for each sample we will:\n",
"\n",
"- estimate the model;\n",
"- forecast one period ahead;\n",
"- calculate the error between the forecast and the true value;"
]
},
{
"cell_type": "code",
"execution_count": 159,
"metadata": {},
"outputs": [],
"source": [
"forcast_errors <- NULL\n",
"mdl_params <- NULL"
]
},
{
"cell_type": "code",
"execution_count": 160,
"metadata": {},
"outputs": [],
"source": [
"k <- floor(length(lnyse) * 0.2)"
]
},
{
"cell_type": "code",
"execution_count": 161,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"105"
],
"text/latex": [
"105"
],
"text/markdown": [
"105"
],
"text/plain": [
"[1] 105"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {},
"outputs": [],
"source": [
"for(i in k:1){\n",
" # get the sample\n",
" smpl <- lnyse[1:(length(lnyse) - i)]\n",
" # re-estimate the model:\n",
" tt <- data.frame(tt = 1:length(smpl))\n",
" smpl_mdl <- forecast::Arima(smpl, order = c(5, 1, 0), include.drift = TRUE)\n",
" # calculate the one-step ahead forecast\n",
" smpl_forc_1 <- forecast(smpl_mdl, h = 1) # since we have decided to include the trend as an exogeneous regressor, \n",
" # alternatively - see the code in this file on how to include it automatically\n",
" # calculate the forecast error:\n",
" tmp_e <- lnyse[length(smpl) + 1] - smpl_forc_1$mean\n",
" \n",
" # save the parameters:\n",
" mdl_params <- rbind(mdl_params, coef(smpl_mdl))\n",
" # Save the forecast errors:\n",
" forcast_errors <- c(forcast_errors, tmp_e)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 163,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 0.0176209872949453
\n",
"\t- 0.0199937863583184
\n",
"\t- 0.0249643162052706
\n",
"\t- 0.0105632502253705
\n",
"\t- 0.0224698783618642
\n",
"\t- -0.00552824893065385
\n",
"\t- 0.0298674463416759
\n",
"\t- -0.0238507409866298
\n",
"\t- 0.037985967644067
\n",
"\t- 0.0060780931736808
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 0.0176209872949453\n",
"\\item 0.0199937863583184\n",
"\\item 0.0249643162052706\n",
"\\item 0.0105632502253705\n",
"\\item 0.0224698783618642\n",
"\\item -0.00552824893065385\n",
"\\item 0.0298674463416759\n",
"\\item -0.0238507409866298\n",
"\\item 0.037985967644067\n",
"\\item 0.0060780931736808\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 0.0176209872949453\n",
"2. 0.0199937863583184\n",
"3. 0.0249643162052706\n",
"4. 0.0105632502253705\n",
"5. 0.0224698783618642\n",
"6. -0.00552824893065385\n",
"7. 0.0298674463416759\n",
"8. -0.0238507409866298\n",
"9. 0.037985967644067\n",
"10. 0.0060780931736808\n",
"\n",
"\n"
],
"text/plain": [
" [1] 0.017620987 0.019993786 0.024964316 0.010563250 0.022469878\n",
" [6] -0.005528249 0.029867446 -0.023850741 0.037985968 0.006078093"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tail(forcast_errors, 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The root mean squared errror is:"
]
},
{
"cell_type": "code",
"execution_count": 164,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'RMSE = 0.04047'"
],
"text/latex": [
"'RMSE = 0.04047'"
],
"text/markdown": [
"'RMSE = 0.04047'"
],
"text/plain": [
"[1] \"RMSE = 0.04047\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"paste0(\"RMSE = \", round(sqrt(mean(forcast_errors^2)), 5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The parameter mean is:"
]
},
{
"cell_type": "code",
"execution_count": 165,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"ar1 | ar2 | ar3 | ar4 | ar5 | drift |
\n",
"\n",
"\t0.04456041 | -0.04141763 | 0.01444384 | 0.02751923 | 0.09970742 | 0.006606406 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllll}\n",
" ar1 & ar2 & ar3 & ar4 & ar5 & drift\\\\\n",
"\\hline\n",
"\t 0.04456041 & -0.04141763 & 0.01444384 & 0.02751923 & 0.09970742 & 0.006606406\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"ar1 | ar2 | ar3 | ar4 | ar5 | drift | \n",
"|---|\n",
"| 0.04456041 | -0.04141763 | 0.01444384 | 0.02751923 | 0.09970742 | 0.006606406 | \n",
"\n",
"\n"
],
"text/plain": [
" ar1 ar2 ar3 ar4 ar5 drift \n",
"[1,] 0.04456041 -0.04141763 0.01444384 0.02751923 0.09970742 0.006606406"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t(apply(mdl_params, 2, mean))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and the variance is:"
]
},
{
"cell_type": "code",
"execution_count": 166,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"ar1 | ar2 | ar3 | ar4 | ar5 | drift |
\n",
"\n",
"\t9.209398e-05 | 5.081817e-05 | 0.0001011694 | 9.729149e-05 | 7.961683e-05 | 2.978902e-08 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllll}\n",
" ar1 & ar2 & ar3 & ar4 & ar5 & drift\\\\\n",
"\\hline\n",
"\t 9.209398e-05 & 5.081817e-05 & 0.0001011694 & 9.729149e-05 & 7.961683e-05 & 2.978902e-08\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"ar1 | ar2 | ar3 | ar4 | ar5 | drift | \n",
"|---|\n",
"| 9.209398e-05 | 5.081817e-05 | 0.0001011694 | 9.729149e-05 | 7.961683e-05 | 2.978902e-08 | \n",
"\n",
"\n"
],
"text/plain": [
" ar1 ar2 ar3 ar4 ar5 \n",
"[1,] 9.209398e-05 5.081817e-05 0.0001011694 9.729149e-05 7.961683e-05\n",
" drift \n",
"[1,] 2.978902e-08"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t(apply(mdl_params, 2, var))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can visualize the series as separate plots:"
]
},
{
"cell_type": "code",
"execution_count": 167,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 10)\n",
"options(repr.plot.height = 6)"
]
},
{
"cell_type": "code",
"execution_count": 168,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAALQCAMAAAC323mdAAAAM1BMVEUAAABNTU1oaGh8fHyM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",
"text/plain": [
"Plot with title \"drift\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(3, 2))\n",
"for(i in 1:ncol(mdl_params)){\n",
" plot(mdl_params[, i], main = colnames(mdl_params)[i])\n",
" points(length(mdl_params[, i]) + 1, coef(mdl_4_1)[i], col = \"red\", pch = 19)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The red dot coincides with the **full sample estimate** (we can also use `abline` to draw it as a horizontal line, but we do not want to treat it as a true coefficient value).\n",
"\n",
"We see that as the sample size increases (here the sample size is `T - k + index`), the estimates converge to some value (**maybe if we had more data the values would continue to converge to some unknown value?**). The `drift` estimate exhibits more variation compared to the remaining parameters so it is unclear how stable it would be if we had a larger sample size."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"---\n",
"---\n",
"\n",
"## **[INFO: START]**\n",
"\n",
"We can also use a built-in function to carry out the cross validation for us. We do need to specify our model as a spearate function for this process to work:"
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {},
"outputs": [],
"source": [
"far1 <- function(x, h){\n",
" forecast(Arima(x, order = c(5, 1, 0), include.drift = TRUE), h = h)\n",
"}\n",
"#\n",
"ts_cv_out <- tsCV(y = lnyse, forecastfunction = far1, h = 1)"
]
},
{
"cell_type": "code",
"execution_count": 170,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Jan Feb Mar Apr May\n",
"1952 NA NA NA NA NA\n",
"1953 NA NA NA -0.0326470999 NA\n",
" Jun Jul Aug Sep Oct\n",
"1952 NA 0.0570292521 -0.0717783295 NA -0.0143642770\n",
"1953 -0.0652138685 -0.0002246052 -0.0585932384 \n",
" Nov Dec\n",
"1952 0.0072660919 0.0122336911\n",
"1953 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(ts_cv_out, 20)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this process is long and performs a cross-validation on the **whole dataset**. We can compare the last few values with our manually calculated ones:"
]
},
{
"cell_type": "code",
"execution_count": 171,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 0.0176209872949453
\n",
"\t- 0.0199937863583184
\n",
"\t- 0.0249643162052706
\n",
"\t- 0.0105632502253705
\n",
"\t- 0.0224698783618642
\n",
"\t- -0.00552824893065385
\n",
"\t- 0.0298674463416759
\n",
"\t- -0.0238507409866298
\n",
"\t- 0.037985967644067
\n",
"\t- 0.0060780931736808
\n",
"\t- <NA>
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 0.0176209872949453\n",
"\\item 0.0199937863583184\n",
"\\item 0.0249643162052706\n",
"\\item 0.0105632502253705\n",
"\\item 0.0224698783618642\n",
"\\item -0.00552824893065385\n",
"\\item 0.0298674463416759\n",
"\\item -0.0238507409866298\n",
"\\item 0.037985967644067\n",
"\\item 0.0060780931736808\n",
"\\item \n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 0.0176209872949453\n",
"2. 0.0199937863583184\n",
"3. 0.0249643162052706\n",
"4. 0.0105632502253705\n",
"5. 0.0224698783618642\n",
"6. -0.00552824893065385\n",
"7. 0.0298674463416759\n",
"8. -0.0238507409866298\n",
"9. 0.037985967644067\n",
"10. 0.0060780931736808\n",
"11. <NA>\n",
"\n",
"\n"
],
"text/plain": [
" [1] 0.017620987 0.019993786 0.024964316 0.010563250 0.022469878\n",
" [6] -0.005528249 0.029867446 -0.023850741 0.037985968 0.006078093\n",
"[11] NA"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tail(ts_cv_out[-c(1:(length(log_passengers) - k - 1))], 11)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the errors are the same as from our manual calculations:"
]
},
{
"cell_type": "code",
"execution_count": 172,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 0.0176209872949453
\n",
"\t- 0.0199937863583184
\n",
"\t- 0.0249643162052706
\n",
"\t- 0.0105632502253705
\n",
"\t- 0.0224698783618642
\n",
"\t- -0.00552824893065385
\n",
"\t- 0.0298674463416759
\n",
"\t- -0.0238507409866298
\n",
"\t- 0.037985967644067
\n",
"\t- 0.0060780931736808
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 0.0176209872949453\n",
"\\item 0.0199937863583184\n",
"\\item 0.0249643162052706\n",
"\\item 0.0105632502253705\n",
"\\item 0.0224698783618642\n",
"\\item -0.00552824893065385\n",
"\\item 0.0298674463416759\n",
"\\item -0.0238507409866298\n",
"\\item 0.037985967644067\n",
"\\item 0.0060780931736808\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 0.0176209872949453\n",
"2. 0.0199937863583184\n",
"3. 0.0249643162052706\n",
"4. 0.0105632502253705\n",
"5. 0.0224698783618642\n",
"6. -0.00552824893065385\n",
"7. 0.0298674463416759\n",
"8. -0.0238507409866298\n",
"9. 0.037985967644067\n",
"10. 0.0060780931736808\n",
"\n",
"\n"
],
"text/plain": [
" [1] 0.017620987 0.019993786 0.024964316 0.010563250 0.022469878\n",
" [6] -0.005528249 0.029867446 -0.023850741 0.037985968 0.006078093"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tail(forcast_errors, 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## **[INFO: END]**\n",
"\n",
"---\n",
"---\n",
"---\n",
"\n",
"## A Look at Seasonal ARIMA models\n",
"\n",
"The airpassangers series, which we analysed previously, may also be seasonally integrated. This would require us to repeat the previous steps not only on non-seasonal differences, but on the seasonal differences as well (as well as combining both seasonal and non-seasonal differences). Here we will simply provide the output of the `auto.arima` function:"
]
},
{
"cell_type": "code",
"execution_count": 173,
"metadata": {},
"outputs": [],
"source": [
"mdl_auto = forecast::auto.arima(log_passengers)"
]
},
{
"cell_type": "code",
"execution_count": 174,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: log_passengers \n",
"ARIMA(0,1,1)(0,1,1)[12] \n",
"\n",
"Coefficients:\n",
" ma1 sma1\n",
" -0.4018 -0.5569\n",
"s.e. 0.0896 0.0731\n",
"\n",
"sigma^2 estimated as 0.001371: log likelihood=244.7\n",
"AIC=-483.4 AICc=-483.21 BIC=-474.77"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_auto"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model appears to fit the data quite well. It appears that the series exhibited unit roots in both the seasonal and non-seasonal autoregressive components.\n",
"\n",
"We can forecast the logarithms of the series, as well as plot the fitted values as follows:"
]
},
{
"cell_type": "code",
"execution_count": 175,
"metadata": {},
"outputs": [],
"source": [
"# Set plot options in Jupyter Lab\n",
"options(repr.plot.width = 10)\n",
"options(repr.plot.height = 5)"
]
},
{
"cell_type": "code",
"execution_count": 176,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAJYCAMAAABFOO8oAAAAPFBMVEUAAAAAAP9NTU1oaGh8\nfHyMjIyampqnp6extc6ysrK9vb3Hx8fQ0NDZ2dnb29/h4eHp6enw8PD/AAD///8iy1u0AAAA\nCXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO3diXajuBZAUbUTx5VUyonh//+1zSwJgQZA\ncPHZa72OyzFDPJwHmEGVACCE2nsGACAUwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsEC\nIAbBAiAGwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsECIAbBAiAG\nwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsECIAbBAiAGwQIgBsEC\nIAbBAiAGwQIgBsECIAbBAiAGwQIgBsF6PTel1K37h+pcv/o7+vt/63t+69vOocuf54DVz8ft\noi63hz2pqxq/wbr7nj9/1huJ0mZyGOD3OUZ1/bZ+D7l4CV+P8dFVg/fujv7+v/U9f8cD9ONq\ng/F7qe++/JpT+nY0or+vy9Q6I9GCNAzw3f5lN4J1FryEL+ev1iIjWOqrvaO/v0nYu/5ZN4d+\n9uKt+vnWjuHNmNK3oxHafW/t0tEqIxmCNPzyof1lBOsceAlfzrM/t65FfZ+eq2NtKfRgqdK6\naQ99a9r177lc9FP+PJeQ/g3T+b2OG2Hc97ddt1xlJN0d+i8/nzP6Uz4+zL8MkvESvprfZxeq\n5ZJ2xWv4FA+lan88P/rV1p/v+pZyDn1p7m+T81ffulWN4d1uhHlfNa61RqLVtf/le9s+8y+D\nZLyEr+bZhc9q2aOtwkywvpT6eN76qG8p19D/2i1I3UaofqtUM4brqBHmfdc6KKuMRAvW8Mvr\ntY+Y+adCLF7CV/NcnnlUW3cuzT/7VamPNhRasK71gy7qOgTLHPrL3O5lJuH9e9wI875m8FVG\n0t/hGOCf+ZdBMl7CF/PdbIBqV/fMje7W+tPPV3XX8+P+9dN91q2hr8MW71L/2XM1Yriv+Ypv\nlZEYD7IGeGvnlmCdAC/hi9E2TNX/1nrVF6z98fPbrv/99sGyhu42ZiW25rfeGr7KSGaC9W7t\nsAHJeAlfS782V6/blVqwPtsdNrVgPR/09uzJpeyCZQ9tNyayNc3NVUYyHaxnry6PyfFAGF7C\n1/KlLVENW45+34f9NfVgfTwXqKot712w7KGPH6zqL3sbfSEKsXgJX8ublhx956R+vckI1t/n\ng6qdDbpg2UNra4pVFH6ML/i0kU3dZwRr0UgmgvW4DPuMEawz4CV8Kf+UTt8d4NLtvq4HqzmK\n8LcL1mjobmDnLlTayKbuM4K1aCQTwXrXR0awToCX8KXchqNqvprPcvcp/tdtnhqC9dssUr01\nhz+7hn5vt5d/u3ZS10Y2cV+zy9UqI3EH60NbviJYp8BL+FJUu6m9bA60K7VP8XV0LGE5nJqh\nf6w59EcXF/0wQFc63Ms//+o9U1cZifOXP8PioD08hOIlfCV/mw9341ovL/Wf4l9lfPPX/KgO\nJP7u/jUeutvn0zjRQnhrzB1HF43E+csPgnU6vISv5L3b2arS7AQ6fIpvxrpV8+OhV2w89LCB\nXDuVVXhrml1GVxmJ85cXgnU6vIRY4OJqQOh9pXnw87KRBNSIYJ0ALyEWuOkLXa2HvVvCxH3V\nQlp3epnlIyFYr4GXEAv8Gl/DNb7sb/km7ut2vFpnJMOan5vv95CBlxBLDCdmH+5yZcVx3+gU\nyYtGQrBeAy8hlhjvlx5sfBGKJSMhWK+BlxCAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQL\ngBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AY\nBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGBmC\npQDAIaEm6wdqh0kAkIdgARCDYAEQg2ABEINgARCDYAEQg2ABEINgARCDYAEQg2ABEINgARCD\nYAEQg2ABEINgARCDYAHI4t5YNA6CBSALggVADIIFQAyCBUCK+32FYhEsADkQLABiECwAYhAs\nAFLcCRYAKe6rFItgAciAYAEQg2ABkOJOsABI8ezUn8aiYhEsANsjWADEIFgApLgTLABSDL2q\nipU+HoIFYHNmsNKLRbAAbI5gAZDiTrAASKH3imABODQjWEuKRbAAbOxOsABIQbAAiGH2imAB\nODCCBUAKa41wSbEIFoBtESwAYti9+pN+Fj+CBWBbBAuAFKM1wgXrhAQLgMeyc7G7g5U2NoIF\nwGNxsP4QLACZEKzdJwEg1KJgOdYI/ySPjmABmLfsgoKOXqUvYhEsAPPWCdZ/LYIFYEMbBStl\ndAQLwLx7txqXNPAQLO0HwQKwieGKgmlDt4MLDdbXm1LX700nAWA92iVQk4Y2FrD+LFsnzBgs\nVQ/4rmq3TSYBYHWvHKybuj3K8vemvraYBIDV9XslpBTG3oS1cJ0wd7Au6lHdfqi3LSYBYG36\nFQVThjY3YS1cxModLKW0f6w+CQBrWydYfa9kBeujC9Zli0kAWJtxzeb4gQUH6/r59a3+Pm8+\nbvNb3QkWcBTGNZujBx6tEfa3jh+sRn3z8thiEgBWdl8SLMcC1rJFrJz7Yf38fH1dr/Wm99ts\nrwgWcBTmJVBjh5UcrENNAkAI65rNkcPOBCtpnZBgAZhhXQI1atC7YxOWO1ih4yVYAKZVxRnO\nsxAVrLt7AcsIVje+oweL/bAACdKDdZ8KlmsRS16wlG6NSQBYrAlW35nwYN1jghUcQlYJAUyq\ng6MHK7QsRq8IFoAMtAWsqGDdZxawhn8SLAArSgzWfTZYo0Ws8P0bcgbrcasOIPx8U+r970aT\nALAmPVjhG7GsXskM1u9FqfJxabaqv28yCQBr0jdhhQfr7lnAGq0THjJYH+r6eP7n4/fZrg8O\nfgaOz1jACl4n9C1g2cGK2OU968HPj/Y/1Qn8OL0McHgLg2X3yRWs+3GDVVZnHNX+sfokAKzJ\nWCNsg+VvizdY1kasYwbrQ/2U5Wf1n2oJa3YjFsECVlQkDmduwgpdxJrqlWurVpWq+zGD9aMu\nt5/yenkW6/tNzV7oi2ABq6g+SkWxJFj2YcvhwXItTrV3SwhW+X0Zjr353GYSAHRKVYtX6wbL\nFxerV75g3Y8arLL8+/FW1er6+bvZJAD0nrmqY5VYLGuNMCxYdq+ME/ZNBetP8B8UjT3dASFU\n0XzBlRasfhNWV5qIYLk3sDs3YhEsABVVl0otCFZdlntMsaxeESwAYdpQqYzBsntlrxE61wn/\nECzg5amFwTLWCMOD9cfRKytYo30dQv+i+L+CYAEyLAvW3R0sT7EIFoAkfaeSimWvEW4SrD/t\nPYHzRLCA01onWHpqJtcJ+5OzTwTrbgXLCBnBAqAWBqtfIyz7belTi1j9Xf4FLMc6IcECMFQq\nJVhan0Z32MGqO9Tdig7WH4IFYOVglZ5gdQtiU2uEpblT6VAsggVA3100oVjDJqv+nq4ydrG6\nRafxApYVrFJ7BMECMFCLgnU3NmH1d7kWsYaVvdk1Qn3E+q/+ECwAeqPSgmWuEQYEa2qNUB/C\nXsQiWAAWBus+XiM01gnNh071arxG6FgnJFjASSz5KBST//C7+4J1Nx4asIBFsICTU/PXPphn\nJipyEevuWCOMD9Z/jjXCYSOWUazA+SJYwFGpRR+FJcG6TwTLtU7YdsoRrP9cC1gECzijZukq\n/bOwIFh39xqhM1h9pqZ7NQqWY50wcM4IFnBI9YegKJI/C9aQMcHqyjO+5sRUsPos3V29sr5V\nJFjA6VQnNi7s7ESwAxUerLu2gDUOll2soVJmsLReTQVLL1bgvBEs4Ijay0fsEKz79AKWI1h6\npWZ6Ze23RbCAU+lW4VKv0DUaMHSdcNgU5QrWaJ3QWKrSSqSv7hEs4OT6YCV+GEbDBQbL7JUr\nWPYpHPTt7P3GKWMfq/toLOONWIF/FsECjqjLS3Kw7DvCgqV91ecK1midcLRru7066FjAcm7E\nCvyzCBZwQGr1YAWtXOq7JjivSx8SLKtXQcH677+wP4tgAQdUOG4ljiBmRPom9Mlg6cte7mCZ\n/7Z75dqIRbAAwZYGyzFUyDqh1StHsMyNWBNrhAQLeClasJI+DenB0rPjOnd7n5nQYI3WCB1b\n3UN7RbCAA9LaslqwApbVzB2pXMGy1gnT1gjHG7EIFiBYMXE7aQThI7pb2fEFK3GNkGABZ2Is\nVaUEyzmMf53Q3lF9jWA51ghH64TP/wb+YQQL2MSiU+/tEyx9A9ZEr0pjJ/jANUKCBRzbolPv\nLTpX6MwwMcH64w3Wn3vqGuFonZBgAXtaeOo9c9j4Yk0sS3mDZUXHlZpyIlj/WcN6g6UtYlX/\nC/3LAh+3bJADTgLYzOJT7y0N1tQQ82PSD12e7JWxTmivQ4auERIs4DCU8SNeUe4arP7I5YBg\nab2aDpZ7LAQLOITFwbKGjA7W5NZ1T7Cs9viCZZxNZthBITRY/SHW9SChf1rg45YNcsBJABtR\n1s9odrCiryk4HazZebobuWp2ZXc8Sj86R1sf/K/bfB6wRmiuExIsYD/Vu7co1jsbe/wi1vTj\nXb/RLyFv9ModLH2dUOvV8H2f3SuCBRyYKpad3NjehLVqsBwz1Z+KzzoxTGiwjM1X4zNhTS6n\n3Y3BA/80ggWsSnW9WO1cobHBmlmFdAeracrdys10sIYDoPVe1ctK415Nj4VgAbtbfuq90XCR\nG7HmHu74VRuVuxWsqdIYZ2wwVwLHZ3IPCtYfggXsZfdgzT7aMVPthnErWJOlmQmWdSnCuV4Z\npwokWECKoj6mZtHbTw0LMaudKzRmTErNPtoVrKZYo17NBEsrlrESaFzqeT5YJcECFmo2ly8L\n1gYnN44Yk/I8erxFv+z6osdnrjTmIpa9H4OVK4IFbKVa/FharMXBcq1JBqwTNo9Q3umOR+8I\n1mxpCNYekwBG6k964VgIiaC3Je3Ue0uDNf9YZ7D+OHo1G6z+0a5e/QnplV0s7x9Y9n9gJIKF\nk1q4P0LF2IK02rlC/WMqhkXDlGD90YLlLY2+ESt5AYtgAcssvdiyPo7xP0JtHazRp6utjHbO\nGE+vtHVC7wIWwQI2Mny9l/4G3ChY3jEVfYq8j7T/OH1H9YDOVMKDNTsSggWkWyFY5j4FcoPl\nGUe/Ecu3Rugby51gAWnUGsEycjG/S5TbxBCeETVfF6QFS/++LyhXZb+XqW8ByzcSggWkWr4H\n1WhJKGERa0mwAh7oeIR2YpjAXPXrhJ5geUdCsIBExv4Iie9Ae5FqvWB5xpQWrOaW9n1fYK4c\nwRrSE5qr0rwMa9h08wbr3+e1OvBBXW//tpoEkGiVYFm5SFgnTDtZaNFPLCBY/R/XBavfHBWY\nq7I/eZZeKSNYgSM5crAeb2rwvskkgGRGbBLXCZcHK+3sxkU/sYDp9cFqH/unPzFM6PJVaQfr\nbgYrfCRDsQIHyRism7r8/alv/X5f1G2LSQCpzFIcL1jz52BoJtbujeVjnU7iT792Fx0scy2w\nvx0xlj5zgUNkDNZF/fS3f9Rli0kAqawgJBVr1Kf4YMWd3Vj/XXNUTkSwul1I2xOIRq0Ratdc\nHTZanSxYxlk75k/hQbCQmZ2WtGCNhoou1rJghU3N2qG/3ws0ojTaRVe1bwUj1wgPHiyWsHBc\nBwnW3NmNp4cazjARFiyl/yi1rU9hM2kOpe93FbmANQQreKC827C+f+tbbMPC0Yy2PqUUa9Ng\neVoW85nRdjMt9WpEjKK0vhVMC1Y/7SMGq3zXviV8e2wyCbyq5F09W6Mc7BKs2YePf1UMP6M+\nMu5gRZXGHax73BphP+3wofLuh3Wr98O6XD/ZDwvras4VmmxcinUOA9w0WP0m9pRgaWdt6KsR\nM47SGazIBayDB+tIk8C5hO2CNGlcioR1QscgKmq2PKdjH0+t6H4R94mpB9UGaasRNY7yrveq\nbK8qQbCAAEV16YgFC1mOlblVghW1iOWrm+PA6u5onMhPzChY9+gFrHK0G0NCr9pgRQxGsHAG\n9WbnlJMjtBytyRYspd0IDlY7XmWt3QUqrGHSg6WlJiVYXSsPHyz2w8Kams9y0ld7U0PGjyw1\nWO2HwXs+du2X/WibFcOEYBmD1JvLI8cxXpl7rWAp3RqTwAvRPr5JVgmWa4CwJSxVBvRK/3U/\nc8peWAqi7GHiS9NuxBoFK3YkzTeLhw/W7pPAmRSjG3Gcy0arBMtfrPrN/vz/6IDt8/3vtZGq\nlKv8qNHpKBKDZQ5GsIAQWwRrpeOWw4IV9n2iVil9/PEfFzX6iMX3qt3wtTxYUWuSBAsn4Pok\nx3AOFjuu1GB1X276J9enSZ/UOD4Bxltd1ghWWvYOG6zHrTqA8PNNqfe/G00CL0kdOFje0VRb\noYrA3cgK62c9fMqnZY1PmGO/9vRghT48Y7B+L8+n9nHhBH5Y2/LLw3vGmj4S7yJWO5Wwfcic\n3y3sFazScSDOmYL1oa6P538+fp/t+uDgZ6xHX0Fa5xhAe7SRc2GMPChYgZNQ8cNsJ+WrRedI\njhkspR7tf55rh5xeBuvZKFiR45p69PxoCFbUaHKfwO+itH+sPgm8pMVnY18lWGknN46cyLB7\n+wGsEqzIvbeyrhL+lOVncxa/x/xGLIKFCKKDlbAUd6BgrTOWiNFkDNaPutx+yuvlWazvN/W9\nxSTwkowPcMqneWqQ4B05Zyc8uxErdrVTxQ+znXMHq/y+DMfefG4zCbwgFdaNGWnLRtZXe9OP\nnRtNyleRR+nV2YNVln8/6msTXj9/N5sEXs7i690krsxZ5+DKFqzDLGAl7MTgGklU9tjTHdJZ\nH+B1zrIQMipzaSctWLEz+1wnPFmw4pbTCBak2y5YnpwYwUqskuhgrYNg4ZUsv3xE2rLRcH5i\n70Onf5dySoiT9SpuOY1gYWdLX+zRZz46AouCZf2IHE1CsM62gEWwIMrS0zXuGKz2gqSFd0t4\n4jqnc4jTBSsKwcLOdg9W6jbxYpj1wnOVsdEv1dQvvM63ShiFYGFf7QmCkz+FaSc31t9haStz\nzQLWcPa9+clZo+nOYbXmTmOvgWBhX83pzNOv0JUYrGG5bvbRvmB14fFNjmCthGBhX/VrXaR/\nDtOC1Z8IXanZVnqDpVVrdnrmWMvh70YUgoV91euDISc0nxo+JVjNWT6rXZp8i3bmuLRtVcWw\ndBXwdtX2L20sXBF+WQQLu2o/tsnXQE07uXG7C1XAiqgyUjMMq11cK+TdOoym0P5mghWNYGFX\n3ac29cv6JcGKHL+931XMu1SNFsyq4V97D4UkBAu76hatUhex8gXLvFFEvktHwXousNGreAQL\nuzKuuZ4yfEqwYqalLxtpt2KvXjqMZRgu/avR10WwsKulwXIPFXCahVBWsFS7ASo2WN1ojOEI\nVjSChT0Na4JpwUo7uXFqsOq9t9SSYCVcVh46goU9aZuuMl7vJiVY/YE49SJW7Cas4dwOvLcX\nIVjY09JgTQzj2YQfNaXRspEqU8LTjKbgrb0MwcKeNgpW0HlhAnXBGo7l0f4bORoWsJYiWNiT\nHpaEYKWd3HhhsIZDcqJHQ7CWIljYkbHqlrCIlSNY3X5XZrDi36J1sHhnL0SwsCNzW1NQSIrJ\nf0yP2BpD5NtLjVKjUt6i1fGLvLOXIljYUUqwwoaYPc1CnBWDxRt7KYKFHamw5SXzQcPDZqq0\nYrAcK3NBZ2gYzxHBWoxgYT/2iltASup4BOxsunKwrNQkndaZYK2AYGE/KcHqjo0p57esOzZi\ndXuARr+7HMtGKe9QRa+WI1jYT1Kw6gNk+tPgTY/b+mV/coRVgpWCYK2AYGE/o2CFnmtY+dfJ\n7FOF9qefStjda50r1aRs+IKFYGE/8RdtDl9IMcbdHvpXn789JVjrLBvxtl6OYGE34+1MawZL\nH1l/yYm09qy0MsfbejmChd04guV75SPKYZzcWHVTTNsaxYmrjoJgYTfT3+RNSjlVqHngctJ7\nizfkURAs7MaxW4InSDGLR85gpe1BhcMgWEhXv07Jq0uu4/1WDJbr+hEl7y3hCBbSVYsrCy4y\n78qT51ShScFi/6fzIFhIppropBYrJVhR4ydY50OwkKw9SCY5WK4BVwyWfi1AnATBQrI6WOkX\nmXcPOHvmvbg3xnD9CJwFwUIy1exCnjFYkVNIPXgQh0WwkKpdI1z1IvOrBqu/tBZOg2AhlWpb\nsOZF5svZvhCsl0ewkGpZsCYXzNY7Gbvj5MYQjmAhUderdS8yPxuspGkQrDMhWEjUB2vVi8zP\nHbATP5kiaSgcF8FCoq2CNSpMdcLPxFPvEayzIVhINGyESglW8EUilOqyk7Bux5VqzoZgIY3S\nyhJWLONBoRe86Sczfwb36WmygHUqBAtpEoJlhChw7wXty0SCBYKFRPpuCQnBCt0/NPnIn25U\nBOtUCNZr8l4ly0dfwAoLVhE8hPbLhb1ik/vZEKyXtGQP9YYRrKBRGd/YzQ9AsDCBYL2ipleL\nPs1mSYKDpVqhZ5FZFFWcD8F6RVUF2kOXUyUES6l+IM/aKMHChPzB+npT6vq96SQwr+vVgmDZ\ni2f+MRXDJL0bz/pM0SuYMgaruV7Je7NKcNtkEgjR92pBD+xtS/4xtTtwFkEngSdYcMsdrJu6\nPcry96a+tpgEAnQbsPrbKZKDFTZJggW33MG6qEd1+6HetpgEAgwLWAtOxz4aNDhYYeNPPtwZ\n55Y7WN11LOevZ0mwtqMvYK14emPvmFKCxQIWLLmD9dEF67LFJOCnL2BlDFbkMcgEC05Zg3X9\n/PpWf583H7f5re4EazPGAlbqOpdrF64tgkWvYMkarEZ98/LYYhLwMhawUpdhtr7IfDdfBAuW\nnPth/fx8fV2v9ab322yvCNZ2NguWb+f1hGDRK9jY0/3FFNazmy1YkZMgWHAhWK/FWsBKW8Ry\nH5E8fzhzygVvCBZsBOu12AtYKwZrdkwpweLkxhjZK1jsh7WP3YIVPQ1OvQeH4wRL6daYBMZG\nvUop1tQ5qlYNFucKhQurhC9l02DNXQgn5YI3vAswQrBESn2CivGQ2warO+KZYGEVBEui5HVm\nV7BiV72mz1Tq2NehVBO/8U+GNwHGOIGfRKkfZkev4hexpgvnClb6mQJ5E2CME/gJpFKfoY2D\nNRqT6v5DsLAOTuAnTROd0GfI/MbVuVlo62BVA/CCYh2cwE+a5nKCwcFq9hdpB3UP5S+WMm7P\nfBnoHoyzxGAtnMBPmmd1CueqnZPxdKcHSz9ceiZY1pjaDe7LrtgKaDiBnzBFu00o7ClSxq2J\nboQsYfULS9PfEY7GpIgV1sYJ/ITpLj4TG6xSRWx7coxFBW1AN4NFrLC2rMHiBH7LdVdniA7W\nTGlCglUvZnl3UdDHRK6wvpz7YXECvxUU1s95KwWr0EcWHKz5kQIJ2NNdlsJxa4axT0PIWCd+\nXYSGKHL+gDgESxRtCSZkX4HAXoWcLbQIW7QjWNgUwRIlOlj9g2YfPT+ubjt/K3AGCRY2QLAk\n0b/oCzloWQ0rc0uCFTJr9oPZWRRbIFiCmI0KKNZw7ZmwzepOccfVxH0pAMQhWIJEB6t5QOE/\neSfBggwESw5rJ3N/sFRwPeZOFhr5ahS+EQLpCJYco2D5d0cItnaw6BU2QbDksAvlXcSKqMbk\nEpHjLPAhEyVY2ATBEmO0ROULVszGp5lgRb4YBAsbIlhibBqsmdO0x74Y9em6CBY2QbDEiA1W\n3Ld77sQUicGiV9gGwRJjvJF9vljpwep2Z29+ECwcB8GSwvGl4GywIjc+WedZ0A7CiQ6WYo0Q\nWyFYRzWuU1SwEr/dc0w5+sXgIvPYDME6qoBgze/vGfksTh22HP9aECxshmDlE3UKztGn3hms\nuWuaRj6JdrD6y4XEjaYanjVCbIVgZVMMW7ODHh2yhX0qDfWuBRHzpo+q2dLeX3eCYOFACFY2\n+jdvIY8erZmFByvp271uXEWpXXEi6bWgV9gKwcol8jQGxeg4HOeQmwTLWLYiWDgQgpVL0V02\nKOjjPNqZKSJY7UJcYrC0rV/achZwCAQrk74D4cEKOZnMaGzJu091U9D231IpowE2RLAyGTqw\narCse7UtZPHPYXd+UoKFwyJYeegrWiHFsoM1uQNDYf9LaResjTMKVnXrfC8FJCNYeegdCAhW\nYfwo54KlzH8teOraYGljIFg4GIKVhbHcEhYsVcYHK+54Z5tq9qUgWDgugpWFuaLlL1a1nGN8\nLzg9jB6phfsTKDtYpTrfSwHRCFYO1o7n3q4UXSq6R84c5rx2sIznfskaJrA+gpWDvdziC0vR\nfUGXOVjjQxDP9kpAOIKVQ3KwugSFXYZr6R7manwSrbO9EhCOYOVgL7h4g9UfFeMPlraItfiQ\nGDay4+AIVgbjFa35tHTLOcMi1tzjCRZeB8HKYHxyKk+w9IP56g32s8GK24d+Dl8K4uAIVgaL\nglUdbhMWrOWnoSJYODiClcH4ehC+VcJOM5znHFpd31Y4qwu7MeDYCFYGjgvYhG2UqjcqKe8F\nU7uupc2d7mRPPE6HYGUQGyztdsgiTzv6NU5MfLInHqdDsLbnukLg3G4KiRPgTOo4P4K1vvEG\nqyzBolc4P4K1vlGwXH/O9KE28ROsg8UCFl4AwVqfvd3JWZI1g9Wc3IFg4fwI1ursnZncJZnK\nS1J2CBZeBMFanXV8y9SlAyf+xrTsFAQLL4Fgrc4MVuDJ2Ofv9fLsDA+cBMFaXXdmmO4fBAtY\nC8FanR6smd0N4r479LGvbA+cEsEKEXXhLFUUXYyag5fdD7OCVTRS55Bg4SUQrBBK+6//sUWT\nn3I+WI4rCibPn/f4aOAcCFYAZf2cf3DRPLTw9MoO1sITJRAsvAKCFaA7fUtEsKpiec6hsOIV\nBecmA5wIwQrQn5UqZL6GYDX/zhQs4BUQrAD1d31FYFW6/QuU8p2OvZi4DWACwfLr900IWcTq\n94fqFrFmgqWNjWABAQiW37DzZ8Ailr4DZ1HOn0eGYAFxsgbr3+e13p/pevu31SS2MBxdE7CI\nlRYsNmEBITIG61WdmcQAAArySURBVPGmBu+bTGIT+tE1/rDYG6YyXVEQeAkZg3VTl78/9a3f\n74u6bTGJTeiHL/sXsQrrHwQLWE/GYF3UT3/7R122mMQmjPMteBexCBawnYzBMnblnt+vW26w\nrJMmzB/it+IlUIGXwBKWjxpvl5ph/TrwEqgECwiSdxvW9299S9Q2LOsMfJ5FLLs82a7ZDLyC\nnLs1vGvfEr49NpnEBjYNVnfUT/xsAa8o735Yt3o/rMv1U85+WKNThvoSFGPFazYDr4A93T1G\n52SfjUvsDqBcsxmIQbA8IoMVOXaCBcQgWB7jYM3NXFKw6BUQaK9gSdkPy3HVm8DDmcNwCVQg\nwnGCpXRrTGIVjssKzgUrevwEC4hw9lXChRejiQqWSigPwQIinD5Y2n9TuC7cPDG2yWs8zykS\nhwNe0smDVVg/42fEMaR7ZI6tXSG4ZjMQLn+wvt6Uun5vOolBvmCpqV94eE7oAECT/WwN7fE5\ns4cSrhaswnErSnCwUntFsIAIuYN1U7dHWf7e1NcWk7BtEyzHOpxKnwYXmQeC5Q7WRdVHPT/U\n2xaTsBTOmxEmtoeP7lxyCDPBAoLlDla3i1WWHUejL/xnTzcwWItOuUCwgGC5g/XRBSvHCfzi\ng2VNeCJY1jrhspNaLdhJDHg1WYN1/fz6Vn+fNx+3HCfws0+v7qXsa0xM7HFg3t0NkhoeggWE\nyhqs/rAbpS4ZTuAXcx6rZrJFYR4NGBOs5O4QLCBUzv2wfn6+vq7XetP7bbZX6wQr5rQw7WQL\ncw1tch/0VYMFINSJ93SPO1tx/wg1JGtyH3RlVC109AAWOm+wYs6y0E610H+UccGiV8D2CJY2\n1cL8SbCAg3mhYHmbMgrW9AB2sNg3AcjhtMEKPsvCMFF7VXDmNArar5KPIgQQi2ANE7WDNfN4\n7bEsXgHZnCVYIVusgoPV3gwMFrkCcjlNsKzFnLCDls2JEizg4E4SrKIMORJnNi3GFivlO02V\n/5tEAKs7UbCMbUkECzihMwVLa4y7IuHBqv5FsICjOVewfOdwn4uLHaz5i6KO9tkCsL1zBGu0\nZBUfLLs8ynMVZ/++WgDWdrJgea5DGBMszzwQLCC/1wrWTLFG5QkLFr0CMjpFsAr7dnywxrtT\nESzgcE4XrPkL/U0HK7o89RCsEQI5Eax2ggQLOL7zBWv+ulkTv0oNFr0CcjpDsKxqzJ48YSpY\n8eUhWEB2JwzWbEXcv0tas/MevgNgZWcMVvxjk7rjO3oHwNpeLVjOB6dtOidYQG4nCFZcNYx9\ntuxjpqMQLCC31w5Wc94/z1GDk3yHGwJYmfxgxS7laIfxKFWfkT31DyJYQGbigxW9/ck87lDF\nTc2cdI6nAsBAfLCiNyNZB0or32kZpqUPCSCJ9GDFb/a2z+yw4O8hWEBewoOVskOC5yR/EQgW\nkJfsYCXtQLVesADkJTtYSc0hWIBUooOVeHKX9tR7rNAB0ogOVuIyEucKBYQSHaxEBAsQimAB\nEOMVg1Vy6j1AJoIFQAyCBUCMlwzW/HUqABwVwQIgBsECIAbBAiDGawaLXgEiESwAYrxosABI\nRLAAiEGwAIhBsACIQbAAiEGwAIhBsACIQbAAiEGwAIhBsACIQbAAiEGwAIhBsACIcdBgAYBD\nQk3WD9SujvT3MC9OB5oV5mXCkebFdNw5S3Okv4d5cTrQrDAvE440L6bjzlmaI/09zIvTgWaF\neZlwpHkxHXfO0hzp72FenA40K8zLhCPNi+m4c5bmSH8P8+J0oFlhXiYcaV5Mx52zNEf6e5gX\npwPNCvMy4UjzYjrunKU50t/DvDgdaFaYlwlHmhfTcecszZH+HubF6UCzwrxMONK8mI47Z2mO\n9PcwL04HmhXmZcKR5sV03DlLc6S/h3lxOtCsMC8TjjQvpuPOWZoj/T3Mi9OBZoV5mXCkeTEd\nd87SHOnvYV6cDjQrzMuEI82L6bhzBgAWggVADIIFQAyCBUAMggVADIIFQAyCBUAMggVADIIF\nQAyCBUAMggVADIIFQAyCBUAMggVADIIFQAyCBUAM4cH66ub/dlHv3/Ut1ejuvdwex5iXr7fj\nzMvTv1yvvGdWfj6U+vg9xLw89n676E/GkeYl61vXQ3awfroP4Hv9rvts7urfgc29b4eYl1t9\n65LnZffMy9PjkumV98zK93Gelt9LMy956umYF/3J2Putq89L1reuj+hg/Vy6pRf1/igfH+qn\nevKv3a//qctP9Zh/B5iXH/XxqH73cYB5qVxVnlfeNyuX50v0uKrbAeblo56L234vkfZk7P7W\n1eYl61vXS3Kwns9v+0y/16/sb/X0fjX/B1G5qWrp9u9wx47zcm1+mSUTvnkpqyclT7B8s/K3\njsRDXQ4wL2rvl0h7MnZ/62rzkvOt63eMuUjzfE7NN5l6r57+r+73V1Ut3VuLFjvNS/ewHM+3\nf15++/fozrPS/L95Hr55aVeSs8TTOS/ak7H7W3f8whCsxX7s/1esflzV94e63Kx7d5+XxqN6\nLxxgXt7Vb573n29W3lT5ealXOfafl892lTDHUo1zXrQnY/e37uiFyfPW9ZMcrLJ/it/q/0P6\n17wDa+9l3lfdNy+NL/V9hHn5VH/z/R+m5yWq/5FjocY7L+VXtdX9Yi8U55sX7cnY/a07emGy\nvXU9zhGsT3V9lD/vzTP9t/qCulrS3+dVd89L7feSYxHfOy/1mkbuYE29RNW23Y8sSzW+eXne\n3X9HttO89E/GAd665guT763rcY5glfU30to3X4/qG+F9XnX3vNQ3LtmWqmfn5a36hjp3sKZe\nompTyW+u7+9n5+WrWiV8fkYzLWKN50V7MnZ/61ovTMa3rsdJgvV8n10+9de3unnZ51V3zkvl\nPdPH0jMvH/XCffZgOZ+WnT6Yznl5U9UWm0fueA7zoj0Zu791rRcm41vX4yTBqv1o77Vm+0S1\nSv6b5asW37w85+PtPdcO3fPzonq7z0rur8xn52WneA7zoj0Zu791jRcm61vX4xzButT/5/hV\nvb7Nzfql/qwXJb7z7JXomZfnbORcqJ6bl32CNfcS/eZ6bmbnpVmqybNPmHNetCdj97eu/sLk\nfet6nCNY9e7J/96qDai3ektEveNd1t2FPfOS7TMZMC/6I3aelV/1Vu9b/fcA8/K8+Wjv2Gde\ntCdj97euNi+Z37oe5wjWozkM7DrcbPfyMfcq2HFePrIu1XieF+0Re8/K53FeovZIuv3mRX8y\n9n7ravOS+a3rcYy5SNY9i7/PZ/XaLDxUx9y/ffU3L5n+D9MzL3lXwzzPi/6IvWfl+/0oL1F7\nhoQd50V7MnZ/6w7zkvmt63GMuQCAAAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AY\nBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQL\ngBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AY\nBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQL\ngBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AY\nBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQLgBgEC4AYBAuAGAQL\ngBgEC4AYBAuAGP8D5b446aZUZJQAAAAASUVORK5CYII=",
"text/plain": [
"Plot with title \"ARIMA(0,1,1)(0,1,1)[12]\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(forecast(mdl_auto), main = forecast(mdl_auto)$method)\n",
"lines(fitted.values(mdl_auto), col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to get the original values, we would need to take exponents of appropriate elements from the `forecast(mdl_auto)` variable. A more convenient way is fitting the original series and specifying a logarithmic transformation:"
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {},
"outputs": [],
"source": [
"mdl_auto = forecast::auto.arima(airpass, lambda = 0)"
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Series: airpass \n",
"ARIMA(0,1,1)(0,1,1)[12] \n",
"Box Cox transformation: lambda= 0 \n",
"\n",
"Coefficients:\n",
" ma1 sma1\n",
" -0.4018 -0.5569\n",
"s.e. 0.0896 0.0731\n",
"\n",
"sigma^2 estimated as 0.001371: log likelihood=244.7\n",
"AIC=-483.4 AICc=-483.21 BIC=-474.77"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mdl_auto"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can forecast the series, as well as plot the fitted values of the original data:"
]
},
{
"cell_type": "code",
"execution_count": 179,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAJYCAMAAABFOO8oAAAAP1BMVEUAAAAAAP8AZABNTU1o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",
"text/plain": [
"Plot with title \"ARIMA(0,1,1)(0,1,1)[12]\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(forecast(mdl_auto), main = forecast(mdl_auto)$method)\n",
"lines(airpass, col = \"darkgreen\", lwd = 2) # to verify that it is indeed the original series\n",
"lines(fitted.values(mdl_auto), col = \"red\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}