{"id":64,"date":"2023-10-29T19:43:22","date_gmt":"2023-10-29T17:43:22","guid":{"rendered":"https:\/\/web.vu.lt\/tfai\/v.gontis\/?p=64"},"modified":"2023-10-29T20:12:54","modified_gmt":"2023-10-29T18:12:54","slug":"pristatome-savo-naujausia-mokslini-darba","status":"publish","type":"post","link":"https:\/\/web.vu.lt\/tfai\/v.gontis\/2023\/10\/29\/pristatome-savo-naujausia-mokslini-darba\/","title":{"rendered":"Pristatome savo naujausi\u0105 mokslin\u012f darb\u0105."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"301\" src=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/Article_Banner_MDPI_fractalfract-07-00581.png\" alt=\"\" class=\"wp-image-65\" style=\"aspect-ratio:1.9767441860465116;width:841px;height:auto\" srcset=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/Article_Banner_MDPI_fractalfract-07-00581.png 595w, https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/Article_Banner_MDPI_fractalfract-07-00581-300x152.png 300w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><figcaption class=\"wp-element-caption\">Spauskite paveiksl\u0117l\u012f, jei norite atsidaryti straipsnio .pdf byl\u0105.<\/figcaption><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p>Tyrin\u0117dami socialines sistemas ir ypatingai finansines turime pasirinkti prielaidas ir matematin\u012f (stochastin\u0117s laiko eilut\u0117s) ar fizikin\u012f (agent\u0173) model\u012f. Nepaisant to, kad empirini\u0173 duomen\u0173 prieinamumas pasiek\u0117 dar nereg\u0117tas galimybes, tinkamo, teisingo modelio pasirinkimas i\u0161lieka sunkiausiai sprend\u017eiama problema. Pavyzd\u017eiui, tiriame empirines sistemas, ie\u0161kodami jose ilgos atminties ir prognozavimo galimybi\u0173, naudodami matematinius laiko eilu\u010di\u0173 modelius, kuriuose ta atmintis yra i\u0161ankstin\u0117 prielaida. Akivaizdu, kad taip \u012fvertinta tiriamos sistemos atmintis turi prasm\u0119 tik tuo atveju, jei teorin\u0117 prielaida apie tos atminties kilm\u0119 atitinka tikrov\u0119.&lt;\/p><\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p&gt;Savo ankstesniame darbe &#91;1] tyr\u0117me sandori\u0173 pavedim\u0173 srauto finans\u0173 rinkose laiko eilutes, remiantis pa\u010dia bendriausia Trupmeninio L\u2019evy stabilaus stochastinio proceso (TLSSP) prielaida, ir parod\u0117me, kad \u0161ios prielaidos pagrindu turime pripa\u017einti pavedim\u0173 srauto antikoreliacines savybes.  Tiriamas laiko eilutes apibr\u0117\u017e\u0117me pa\u010diu papras\u010diausiu b\u016bdu, sumuodami\npavedim\u0173 apimtis: pirkti &#91;latex]v_k^{+}(t_j)&#91;\/latex] ir parduoti \\(v_k^{-}(t_j)\\) akcijas&lt;\/p&gt;\n<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>\\&#91;\nX(j)=\\sum_{k=1}^{10}(v_{k}^{+}(j)-v_{k}^{-}(j))=V^{+}(j)-V^{-}(j)=\\sum_{i=1}^{j}Y(i).\\label{eq:order-disbalance}\n\\]<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>\u010cia \\(X(j)\\) yra sandori\u0173 (nuomoni\u0173) disbalansas laiko momentu \\(j\\),\nindeksas \\(k\\) \u017eymi 10 kainos lygi\u0173 vir\u0161 ir \u017eemiau pirkti-parduoti\ntarpo, \\(V^{+}(j)\\), \\(V^{-}(j)\\) atitinkamai rei\u0161kia bendras apimtis\npirkti ar parduoti akcijas momentu \\(j\\), \\(Y(i)\\) yra disbalanso poky\u010diai,\nkurie atsiranda d\u0117l prekiautoj\u0173 teikiam\u0173 pavedim\u0173 pirkti parduoti\nakcijas.<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p&gt;Visd\u0117lto, detalesnis tyrimas parod\u0117, kad pasirinkta matematin\u0117 prielaida yra nepakankama, kai pavedim\u0173 srautas apima ir j\u0173 at\u0161aukim\u0105 bei \u012fvykdym\u0105. Tyrimui taikom\u0105 model\u012f turime tikslinti, atsi\u017evelgdami \u012f pavedim\u0173 gyvavimo laik\u0173 laipsninio pob\u016bd\u017eio skirstin\u012f. \u0160\u012f empirin\u012f pasteb\u0117jim\u0105 si\u016blome interpretuoti, kaip dar vien\u0105 finansini\u0173 laiko eilu\u010di\u0173 stilizuot\u0105 fakt\u0105. Empiri\u0161kai nustatyt\u0105 gyvavimo laik\u0173 statistin\u0119 savyb\u0119 iliustruojame dviem \u017eemiau pateiktais histogram\u0173 paveiksl\u0117liais.&lt;\/p&gt; <\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"558\" height=\"206\" src=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig1.png\" alt=\"\" class=\"wp-image-66\" srcset=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig1.png 558w, https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig1-300x111.png 300w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><figcaption class=\"wp-element-caption\">Pav. 1. AMZN ir MA akcij\u0173 pavedim\u0173 gyvavimo laik\u0173 histogram\u0173 pavyzd\u017eiai. Empiriniai skirstiniai yra suskai\u010diuoti keturiems pavedim\u0173 kain\u0173 lygiams vieno m\u0117nesio duomen\u0173 laikotarpiui. Raudonas grafikas yra pirmam kainos lygiui, m\u0117lymas antram, \u017ealias tre\u010diam ir juodas ketvirtam.<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"554\" height=\"207\" src=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig2.png\" alt=\"\" class=\"wp-image-67\" srcset=\"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig2.png 554w, https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-content\/uploads\/2023\/10\/fig2-300x112.png 300w\" sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><figcaption class=\"wp-element-caption\">Pav. 2. AMZN ir MA akcij\u0173 pavedim\u0173 gyvavimo laik\u0173 histogram\u0173 pavyzd\u017eiai. Empiriniai skirstiniai suskai\u010diuoti keturiems skirtingiems pavedim\u0173 dyd\u017eio intervalams. Did\u0117jimo tvarka: raudonas, m\u0117lynas, \u017ealias ir juodas grafikai.&nbsp;<\/figcaption><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p&gt;Kadangi pavedim\u0173 gyvavimo laik\u0173 skirstiniai akivaizd\u017eiai yra laipsninio pob\u016bd\u017eio (grafikai yra dvigubai logaritminiane mastelyje), pasinaudojome galimybe pasitelkti neekstensyvi\u0105j\u0105 Tsallio statistik\u0105, t.y., parod\u0117me, kad q-eksponentinis Tsallio skirstinys puikiai apra\u0161o empirin\u012f gyvavimo laik\u0173 pasiskirstym\u0105. Papildydami \u0161i\u0105 empirin\u0119 statistin\u0119 savyb\u0119 pavedim\u0173 apim\u010di\u0173 (volume) laipsniniu empiriniu pasiskirstymu, suformulavome paprast\u0105 disbalanso laiko eilut\u0117s model\u012f, kuris esmingai pakeit\u0117 anks\u010diau naudot\u0105 Trupmenin\u012f L\u2019evy stabil\u0173 stochastin\u012f proces\u0105.&lt;\/p&gt;<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p&gt;Pasirod\u0117, kad ankstesn\u0117 TLSSP prielaida visai neblogai tinka tuo atveju, kai laiko eilut\u0119 formuojame tik i\u0161 akcij\u0173 rinkai pateikiam\u0173 pavedim\u0173, bet i\u0161imame j\u0173 at\u0161aukimus ir \u012fvykdytus sandorius. Tod\u0117l atkreipiame d\u0117mes\u012f, kad \u0161is konkretus empirin\u0117s laiko eilut\u0117s pavyzdys gra\u017eiai demonstruoja, kaip yra svarbu \u012fsitikinti ar tyrimams naudojamos matematin\u0117s prielaidos yra tinkamos tiriamam objektui. M\u016bs\u0173 nuomone, empiriniuose laiko eilu\u010di\u0173 tyrimuose labai da\u017enai prielaid\u0173 galiojimas n\u0117ra tinkamai patikrinamas, o gaunami rezultatai, ypatingai ilgos atminties aspektu, yra klaidinantys. Tik pagr\u012fstai \u012fvertin\u0119 ilgos atminties egzistavim\u0105 fizin\u0117se, socialin\u0117se ar finansin\u0117se sistemose, galime tik\u0117tis s\u0117km\u0117s, prognozuodami laiko eilu\u010di\u0173 eig\u0105 ar skai\u010diuodami rizikas. &lt;\/p&gt;<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;p&gt;\u0160is darbas gali b\u016bti prasmingai prat\u0119stas, jei pabandytume apjungti \u0161iuos rezultatus su m\u016bs\u0173 grup\u0117s koleg\u0173 publikacija &#91;2]. Yra tik\u0117tina, kad pavedim\u0173 laik\u0173 laipsniniai skistiniai stebimi tod\u0117l, kad rinka statisti\u0161kai apjungia labai \u012fvairius agentus, prekiaujan\u010dius labai skirtingu intensyvumu, t.y., turin\u010dius skirtingus charakteringus j\u0173 pavedim\u0173 gyvavimo laikus. Kvie\u010diame susidom\u0117jusius fizikos matemtikos studentus bei jaunus mokslininkus bendradarbiauti, t\u0119siant prad\u0117tus darbus.&lt;\/p&gt; <\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Literat\u016bra.<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>V. Gontis.&nbsp;<em>Order flow in the financial markets from the perspective of the Fractional L\u00e9vy stable motion<\/em>.&nbsp;Communications in Nonlinear Science and Numerical Simulation&nbsp;<strong>105<\/strong>,&nbsp;2022, psl.&nbsp;106087.&nbsp;<a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1007570421003993\">https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1007570421003993<\/a>.&nbsp;<a href=\"http:\/\/dx.doi.org\/https:\/\/doi.org\/10.1016\/j.cnsns.2021.106087\">doi: https:\/\/doi.org\/10.1016\/j.cnsns.2021.106087<\/a>.<\/li>\n\n\n\n<li>A. Kononovicius, B. Kaulakys.&nbsp;<em>1\/f noise in electrical conductors arising from the heterogeneous detrapping process of individual charge carriers<\/em>. (under review).&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2306.07009\">arXiv:2306.07009 [math.PR]<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Literat\u016bra.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,3],"tags":[],"class_list":["post-64","post","type-post","status-publish","format-standard","hentry","category-mokslas","category-moksliniai-straipsniai"],"_links":{"self":[{"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/posts\/64","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/comments?post=64"}],"version-history":[{"count":3,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/posts\/64\/revisions"}],"predecessor-version":[{"id":71,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/posts\/64\/revisions\/71"}],"wp:attachment":[{"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/media?parent=64"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/categories?post=64"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/web.vu.lt\/tfai\/v.gontis\/wp-json\/wp\/v2\/tags?post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}