The L2-structures of standard and switching-regime GARCH models

Christian Francq; Jean Michel Zaköan

doi:10.1016/j.spa.2005.04.005

The L²-structures of standard and switching-regime GARCH models

Christian Francq
, Jean Michel Zaköan

Research output: Contribution to journal › Article › peer-review

Abstract

This paper analyzes the probabilistic structure of Markov-switching GARCH(p,q) models, in which the volatility process is driven by a finite state-space Markov chain. We give necessary and sufficient conditions for the existence of moments of any order. We find that the squares and higher order powers of the process have the L² structures of ARMA processes, and hence admit ARMA representations. These results are applicable to standard GARCH models and have statistical implications in terms of order identification and parameter estimation.

Original language	English
Pages (from-to)	1557-1582
Number of pages	26
Journal	Stochastic Processes and their Applications
Volume	115
Issue number	9
DOIs	https://doi.org/10.1016/j.spa.2005.04.005
Publication status	Published - 1 Sept 2005
Externally published	Yes

Keywords

ARMA representation
GARCH
HMM
Markov-switching models

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10.1016/j.spa.2005.04.005

Cite this

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abstract = "This paper analyzes the probabilistic structure of Markov-switching GARCH(p,q) models, in which the volatility process is driven by a finite state-space Markov chain. We give necessary and sufficient conditions for the existence of moments of any order. We find that the squares and higher order powers of the process have the L2 structures of ARMA processes, and hence admit ARMA representations. These results are applicable to standard GARCH models and have statistical implications in terms of order identification and parameter estimation.",

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AB - This paper analyzes the probabilistic structure of Markov-switching GARCH(p,q) models, in which the volatility process is driven by a finite state-space Markov chain. We give necessary and sufficient conditions for the existence of moments of any order. We find that the squares and higher order powers of the process have the L2 structures of ARMA processes, and hence admit ARMA representations. These results are applicable to standard GARCH models and have statistical implications in terms of order identification and parameter estimation.

KW - ARMA representation

KW - GARCH

KW - HMM

KW - Markov-switching models

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -

The L²-structures of standard and switching-regime GARCH models

Abstract

Keywords

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