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/
[1] and, Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Statist. 30 (1966) 1554-1563. | MR | Zbl
[2] , Estimation des degrés d'un ARMA multivarié, Pub. IRMA, Vol. 4. Lille (1982).
[3] and, Time Series: Theory and Methods. Springer-Verlag, New York (1991). | MR | Zbl
[4] and, Stationarity of Multivariate Markov-switching ARMA Models. J. Econometrics 102 (2001) 339-364. | MR | Zbl
[5] , A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (1989) 357-384. | MR | Zbl
[6] , Specification testing in Markov switching time series models. J. Econometrics 45 (1996) 39-70. | MR | Zbl
[7] , A class of non-linear time series models, Ph.D. Thesis. University of Bergen, Norway (1990).
[8] and, Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48 (1992) 545-558.
[9] and, Markov chain models, time series analysis and extreme value theory. Adv. Appl. Probab. 28 (1996) 405-425. | MR | Zbl
[10] , and, Bayesian inference in hidden Markov models through the reversible jump Markov Chain Monte-Carlo method. J. Roy. Statist. Soc. B 62 (2000) 57-75. | MR | Zbl
[11] , Estimating the orders of hidden Markov models. Statistics 26 (1995) 345-354. | MR | Zbl
[12] and, Autocovariance structure of Markov regime switching models and model selection. J. Time Ser. Anal. 22 (2001) 107-124. | MR | Zbl
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