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Autocovariance structure of powers of switching-regime ARMAProcesses

Published online by Cambridge University Press:  15 November 2002

Christian Francq  and
Jean-Michel Zakoïan
Christian Francq
Affiliation:
Université du Littoral-Côte d'Opale, LMPA J. Liouville, Centre Universitaire de la Mi-Voix, 50 rue F. Buisson, BP. 699, 62228 Calais Cedex, France; Christian.Francq@lmpa.univ-littoral.fr.
Jean-Michel Zakoïan
Affiliation:
Université de Lille 3 and CREST, 15 boulevard Gabriel Péri, 92245 Malakoff Cedex, France; zakoian@ensae.fr.
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Abstract

In Francq and Zakoïan [4], we derived stationarity conditions for ARMA(p,q) models subject to Markov switching. In this paper, we show that, under appropriate moment conditions, the powers of the stationary solutions admit weak ARMA representations, which we are able to characterize in terms of p,q, the coefficients of the model in each regime, and the transition probabilities of the Markov chain. These representations are potentially useful for statistical applications.

Keywords

ARMA representationhidden Markov modelsMarkov-switching modelsidentification.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 259 - 270
Copyright
© EDP Sciences, SMAI, 2002

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