Volume 6, 2002
New directions in Time Series Analysis (Guest Editor: Philippe Soulier)
|Page(s)||259 - 270|
|Section||New directions in Time Series Analysis (Guest Editor: Philippe Soulier)|
|Published online||15 November 2002|
Autocovariance structure of powers of switching-regime ARMA Processes
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.
2 Université de Lille 3 and CREST, 15 boulevard Gabriel Péri, 92245 Malakoff Cedex, France; email@example.com.
In Francq and Zakoïan , 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.
Mathematics Subject Classification: 62M10
Key words: ARMA representation / hidden Markov models / Markov-switching models / identification.
© EDP Sciences, SMAI, 2002
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