Autocovariance structure of powers of switching-regime ARMA processes

Christian Francq; Jean-Michel Zakoïan

ESAIM: Probability and Statistics (2002)

  • Volume: 6, Issue: 3, page 259-270
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Francq, Christian, and Zakoïan, Jean-Michel. "Autocovariance structure of powers of switching-regime ARMA processes." ESAIM: Probability and Statistics 6.3 (2002): 259-270. <http://eudml.org/doc/245060>.

@article{Francq2002,
abstract = {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.},
author = {Francq, Christian, Zakoïan, Jean-Michel},
journal = {ESAIM: Probability and Statistics},
keywords = {ARMA representation; hidden Markov models; Markov-switching models; identification},
language = {eng},
number = {3},
pages = {259-270},
publisher = {EDP-Sciences},
title = {Autocovariance structure of powers of switching-regime ARMA processes},
url = {http://eudml.org/doc/245060},
volume = {6},
year = {2002},
}

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
PB - EDP-Sciences
VL - 6
IS - 3
SP - 259
EP - 270
AB - 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.
LA - eng
KW - ARMA representation; hidden Markov models; Markov-switching models; identification
UR - http://eudml.org/doc/245060
ER -

References

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  9. [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. Zbl0853.62068MR1387884
  10. [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. Zbl0941.62090MR1747395
  11. [11] T. Rydén, Estimating the orders of hidden Markov models. Statistics 26 (1995) 345-354. Zbl0836.62057MR1365683
  12. [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. Zbl0966.62064MR1816319

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