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Estimating the number of regimes in a switching autoregressive model

Abstract

In this paper we are interested in estimating the number of regimes in a switching autoregressive model. The penalized marginal-likelihood criterion for mixture models and hidden Markov models introduced by Keribin (2000) and, respectively, Gassiat (2002) is extended to autoregressive models with independent regime changes for which a penalized-likelihood criterion is proposed. We prove the consistency of the estimate under some hypothesis which involve essentially the bracketing entropy of the generalized score-functions class and we verify these hypothesis in the Gaussian case by reparameterizing the model to avoid non-identifiability problems. Some numerical examples illustrate the result and its convergence properties. Finally, we prove that a direct generalization of the "marginal likelihood" criterion to switching Markov models is not possible.
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Dates and versions

hal-00137438 , version 1 (19-03-2007)

Identifiers

  • HAL Id : hal-00137438 , version 1

Cite

Madalina Olteanu, Joseph Rynkiewicz. Estimating the number of regimes in a switching autoregressive model. 2007. ⟨hal-00137438⟩
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