Estimating Components in Finite Mixtures and Hidden Markov Models

Donald Poskitt and Jing Zhang

No 10/04, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests estimating the number of states of the unobservable Markov chain by determining the number of mixture components in the marginal distribution. We therefore present new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi-likelihood and generalized quasi-likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. We show that, under fairly general regularity conditions, the methods proposed will generate strongly consistent estimates of the unknown number of states or components.

Keywords: Finite mixture; hidden Markov process; model selection; number of states; penalized quasi-likelihood; generalized quasi-likelihood ratio; strong consistency. (search for similar items in EconPapers)
JEL-codes: C51 C52 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2004-03
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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