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Autocovariance structure of powersof 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 forARMA(p,q) models subject to Markov switching. In this paper, weshow that, under appropriate moment conditions, the powers of thestationary solutions admit weak ARMA representations, which we areable to characterize in terms of p,q, the coefficients of themodel in each regime, and the transition probabilities of theMarkov chain. These representations are potentially useful forstatistical applications.

Keywords

ARMA representationhidden Markov modelsMarkov-switching modelsidentification.

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