Autocovariance structure of powers of switching-regime ARMA Processes

Christian Francq; Jean-Michel Zakoïan

ESAIM: Probability and Statistics (2010)

  • Volume: 6, 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 (2010): 259-270. <http://eudml.org/doc/104292>.

@article{Francq2010,
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},
month = {3},
pages = {259-270},
publisher = {EDP Sciences},
title = {Autocovariance structure of powers of switching-regime ARMA Processes},
url = {http://eudml.org/doc/104292},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Francq, Christian
AU - Zakoïan, Jean-Michel
TI - Autocovariance structure of powers of switching-regime ARMA Processes
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 6
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/104292
ER -

References

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  1. L.E. Baum and T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Statist.30 (1966) 1554-1563.  
  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).  
  4. C. Francq and J.-M. Zakoïan, Stationarity of Multivariate Markov-switching ARMA Models. J. Econometrics102 (2001) 339-364.  
  5. J.D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica57 (1989) 357-384.  
  6. J.D. Hamilton, Specification testing in Markov switching time series models. J. Econometrics45 (1996) 39-70.  
  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. Biometrics48 (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.  
  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. B62 (2000) 57-75.  
  11. T. Rydén, Estimating the orders of hidden Markov models. Statistics26 (1995) 345-354.  
  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.  

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