Estimating Components in Finite Mixtures and Hidden Markov Models
AbstractWhen 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.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/04.
Length: 22 pages
Date of creation: Mar 2004
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Find related papers by JEL classification:
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-05-02 (All new papers)
- NEP-ECM-2004-05-02 (Econometrics)
- NEP-ETS-2004-05-02 (Econometric Time Series)
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