In Francq and Zakoïan [4], we derived stationarity conditions for ARMA 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 , the coefficients of the model in each regime, and the transition probabilities of the Markov chain. These representations are potentially useful for statistical applications.
Mots-clés : ARMA representation, hidden Markov models, Markov-switching models, identification
@article{PS_2002__6__259_0,
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},
doi = {10.1051/ps:2002014},
mrnumber = {1943150},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2002014/}
}
TY - JOUR AU - Francq, Christian AU - Zakoïan, Jean-Michel TI - Autocovariance structure of powers of switching-regime ARMA processes JO - ESAIM: Probability and Statistics PY - 2002 SP - 259 EP - 270 VL - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2002014/ DO - 10.1051/ps:2002014 LA - en ID - PS_2002__6__259_0 ER -
%0 Journal Article %A Francq, Christian %A Zakoïan, Jean-Michel %T Autocovariance structure of powers of switching-regime ARMA processes %J ESAIM: Probability and Statistics %D 2002 %P 259-270 %V 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2002014/ %R 10.1051/ps:2002014 %G en %F PS_2002__6__259_0
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://www.numdam.org/articles/10.1051/ps:2002014/
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