Estimating the number of regimes in a switching autoregressive model

Madalina Olteanu (1, 2) , Joseph Rynkiewicz (1, 2)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne

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.

Mots clés: model selection; switching autoregressive models; penalized likelihood criterion; bracketing entropy

Domaines: Statistiques [math.ST]

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