On random processes as an implicit solution of equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10371740" target="_blank" >RIV/00216208:11320/17:10371740 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.14736/kyb-2017-6-0985" target="_blank" >https://doi.org/10.14736/kyb-2017-6-0985</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2017-6-0985" target="_blank" >10.14736/kyb-2017-6-0985</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On random processes as an implicit solution of equations

Popis výsledku v původním jazyce

Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is linear for AR, ARMA. We consider a general functional dependence, but, existence of a forward and a backward equivalent rewritings of the given functional equation is required. We present a concept of solution construction giving uniqueness of assigned solution. We introduce a class of implicit models where forward and backward equivalent rewritings exist. Illustrative examples are included.

Název v anglickém jazyce

On random processes as an implicit solution of equations

Popis výsledku anglicky

Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is linear for AR, ARMA. We consider a general functional dependence, but, existence of a forward and a backward equivalent rewritings of the given functional equation is required. We present a concept of solution construction giving uniqueness of assigned solution. We introduce a class of implicit models where forward and backward equivalent rewritings exist. Illustrative examples are included.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GBP402%2F12%2FG097" target="_blank" >GBP402/12/G097: DYME-Dynamické modely v ekonomii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Kybernetika

ISSN

0023-5954

e-ISSN

—

Svazek periodika

53

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

7

Strana od-do

985-991

Kód UT WoS článku

000424732300002

EID výsledku v databázi Scopus

2-s2.0-85040744114