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},
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     url = {http://www.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://www.numdam.org/articles/10.1051/ps:2002014/

[1] L.E. Baum and T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Statist. 30 (1966) 1554-1563. | MR | Zbl

[2] A. Berlinet, Estimation des degrés d'un ARMA multivarié, Pub. IRMA, Vol. 4. Lille (1982).

[3] P.J. Brockwell and R.A. Davis, Time Series: Theory and Methods. Springer-Verlag, New York (1991). | MR | Zbl

[4] C. Francq and J.-M. Zakoïan, Stationarity of Multivariate Markov-switching ARMA Models. J. Econometrics 102 (2001) 339-364. | MR | Zbl

[5] J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (1989) 357-384. | MR | Zbl

[6] J.D. Hamilton, Specification testing in Markov switching time series models. J. Econometrics 45 (1996) 39-70. | MR | Zbl

[7] H. Karlsen, A class of non-linear time series models, Ph.D. Thesis. University of Bergen, Norway (1990).

[8] B.G. Leroux and L.M. Puterman, Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48 (1992) 545-558.

[9] D.S. Poskitt and S.H. Chung, Markov chain models, time series analysis and extreme value theory. Adv. Appl. Probab. 28 (1996) 405-425. | MR | Zbl

[10] C.P. Robert, T. Rydén and D.M. Titterington, 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] T. Rydén, Estimating the orders of hidden Markov models. Statistics 26 (1995) 345-354. | MR | Zbl

[12] J. Zhang and R.A. Stine, Autocovariance structure of Markov regime switching models and model selection. J. Time Ser. Anal. 22 (2001) 107-124. | MR | Zbl

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