Asymptotic properties of autoregressive regime-switching models

Madalina Olteanu; Joseph Rynkiewicz

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 25-47
  • ISSN: 1292-8100

Abstract

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The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent regime switches). In this framework, we give sufficient conditions to keep the LRTS tight and compute its the asymptotic distribution. Second, we consider the extension of the ideas in Gassiat [Ann. Inst. Henri Poincaré 38 (2002) 897–906] to autoregressive models with regimes switches according to a Markov chain. In this case, it is shown that the marginal likelihood is no longer a contrast function and cannot be used to select the number of regimes. Some numerical examples illustrate the results and their convergence properties.

How to cite

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Olteanu, Madalina, and Rynkiewicz, Joseph. "Asymptotic properties of autoregressive regime-switching models." ESAIM: Probability and Statistics 16 (2012): 25-47. <http://eudml.org/doc/222475>.

@article{Olteanu2012,
abstract = {The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent regime switches). In this framework, we give sufficient conditions to keep the LRTS tight and compute its the asymptotic distribution. Second, we consider the extension of the ideas in Gassiat [Ann. Inst. Henri Poincaré 38 (2002) 897–906] to autoregressive models with regimes switches according to a Markov chain. In this case, it is shown that the marginal likelihood is no longer a contrast function and cannot be used to select the number of regimes. Some numerical examples illustrate the results and their convergence properties.},
author = {Olteanu, Madalina, Rynkiewicz, Joseph},
journal = {ESAIM: Probability and Statistics},
keywords = {Likelihood ratio test; Switching times series; hidden Markov model; likelihood ratio test; switching times series},
language = {eng},
month = {3},
pages = {25-47},
publisher = {EDP Sciences},
title = {Asymptotic properties of autoregressive regime-switching models},
url = {http://eudml.org/doc/222475},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Olteanu, Madalina
AU - Rynkiewicz, Joseph
TI - Asymptotic properties of autoregressive regime-switching models
JO - ESAIM: Probability and Statistics
DA - 2012/3//
PB - EDP Sciences
VL - 16
SP - 25
EP - 47
AB - The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent regime switches). In this framework, we give sufficient conditions to keep the LRTS tight and compute its the asymptotic distribution. Second, we consider the extension of the ideas in Gassiat [Ann. Inst. Henri Poincaré 38 (2002) 897–906] to autoregressive models with regimes switches according to a Markov chain. In this case, it is shown that the marginal likelihood is no longer a contrast function and cannot be used to select the number of regimes. Some numerical examples illustrate the results and their convergence properties.
LA - eng
KW - Likelihood ratio test; Switching times series; hidden Markov model; likelihood ratio test; switching times series
UR - http://eudml.org/doc/222475
ER -

References

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