Estimating Components in Finite Mixtures and Hidden Markov Models
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.
|Date of creation:||Mar 2004|
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John Wiley & Sons, Ltd., vol. 11(2), pages 195-98, March-Apr.
- Bruce E. Hansen, 1995. "Erratum: The Likelihood ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Boston College Working Papers in Economics 296., Boston College Department of Economics.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
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