Probabilistic properties of a Markov-switching periodic G A R C H process

Billel Aliat; Fayçal Hamdi

Kybernetika (2019)

  • Volume: 55, Issue: 6, page 915-942
  • ISSN: 0023-5954

Abstract

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In this paper, we propose an extension of a periodic G A R C H ( P G A R C H ) model to a Markov-switching periodic G A R C H ( M S - P G A R C H ), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well as the autocovariances of the powers of a M S - P G A R C H process. We thus show how these moments and autocovariances can be used for estimating model parameters using G M M method.

How to cite

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Aliat, Billel, and Hamdi, Fayçal. "Probabilistic properties of a Markov-switching periodic $GARCH$ process." Kybernetika 55.6 (2019): 915-942. <http://eudml.org/doc/297172>.

@article{Aliat2019,
abstract = {In this paper, we propose an extension of a periodic $GARCH$ ($PGARCH$) model to a Markov-switching periodic $GARCH$ ($MS$-$PGA$$RCH$), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well as the autocovariances of the powers of a $MS$-$PGARCH$ process. We thus show how these moments and autocovariances can be used for estimating model parameters using $GMM$ method.},
author = {Aliat, Billel, Hamdi, Fayçal},
journal = {Kybernetika},
keywords = {Markov-switching models; periodic $GARCH$ models; periodic stationarity; higher-order moments; Markov-switching $PGARCH$ models; $GMM$ method},
language = {eng},
number = {6},
pages = {915-942},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Probabilistic properties of a Markov-switching periodic $GARCH$ process},
url = {http://eudml.org/doc/297172},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Aliat, Billel
AU - Hamdi, Fayçal
TI - Probabilistic properties of a Markov-switching periodic $GARCH$ process
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 6
SP - 915
EP - 942
AB - In this paper, we propose an extension of a periodic $GARCH$ ($PGARCH$) model to a Markov-switching periodic $GARCH$ ($MS$-$PGA$$RCH$), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well as the autocovariances of the powers of a $MS$-$PGARCH$ process. We thus show how these moments and autocovariances can be used for estimating model parameters using $GMM$ method.
LA - eng
KW - Markov-switching models; periodic $GARCH$ models; periodic stationarity; higher-order moments; Markov-switching $PGARCH$ models; $GMM$ method
UR - http://eudml.org/doc/297172
ER -

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