On random processes as an implicit solution of equations

Petr Lachout

Kybernetika (2017)

  • Volume: 53, Issue: 6, page 985-991
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Lachout, Petr. "On random processes as an implicit solution of equations." Kybernetika 53.6 (2017): 985-991. <http://eudml.org/doc/294822>.

@article{Lachout2017,
abstract = {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.},
author = {Lachout, Petr},
journal = {Kybernetika},
keywords = {econometric models; ARMA process; implicit definition},
language = {eng},
number = {6},
pages = {985-991},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On random processes as an implicit solution of equations},
url = {http://eudml.org/doc/294822},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Lachout, Petr
TI - On random processes as an implicit solution of equations
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 6
SP - 985
EP - 991
AB - 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.
LA - eng
KW - econometric models; ARMA process; implicit definition
UR - http://eudml.org/doc/294822
ER -

References

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