Autocovariance structure of powers of switching-regime ARMA processes
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 259-270.

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.

DOI : 10.1051/ps:2002014
Classification : 62M10
Mots clés : ARMA representation, hidden Markov models, Markov-switching models, identification 
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     author = {Francq, Christian and Zako{\"\i}an, Jean-Michel},
     title = {Autocovariance structure of powers of switching-regime {ARMA} processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {259--270},
     publisher = {EDP-Sciences},
     volume = {6},
     year = {2002},
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     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps:2002014/}
}
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Francq, Christian; Zakoïan, Jean-Michel. Autocovariance structure of powers of switching-regime ARMA processes. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 259-270. doi : 10.1051/ps:2002014. http://archive.numdam.org/articles/10.1051/ps:2002014/

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