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Estimating the Number of Components of a Mixture Autoregressive Model

Abstract : In this paper we are interested in estimating the number of components of a mixture autoregressive (MAR) model. Usually, when estimating the parameters of such a model, a fixed number of components is considered "a priori", although the general case of an unknown number should be more interesting to study. However, not fixing the number of components leads to non-identifiability problems which complicate the task. Recently, the consistence of a penalized marginal-likelihood criterion for mixture models and hidden Markov models was proven by Keribin (2000) and, respectively, Gassiat (2002). We extend their method to mixtures of autoregressive models 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 in order to avoid non-identifiability problems. Some numerical examples illustrate the result and its convergence properties.
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https://hal.archives-ouvertes.fr/hal-00655590
Contributor : Madalina Olteanu <>
Submitted on : Saturday, December 31, 2011 - 1:38:05 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:36 AM

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  • HAL Id : hal-00655590, version 1

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Madalina Olteanu, Joseph Rynkiewicz. Estimating the Number of Components of a Mixture Autoregressive Model. ESTSP, 2007, France. pp.143-154. ⟨hal-00655590⟩

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