Abstract: This paper proposes a composite likelihood approach as an alternative to the full likelihood approach for the analysis of time series data from hidden Markov models. The proposed method requires correctly specifying only the joint density of pairs of consecutive observations. Hence, the proposed composite likelihood is algebraically simpler than the corresponding full likelihood while it retains the information on transition probabilities. The proposed maximum composite likelihood estimator with a regularization term added to the composite likelihood is consistent, asymptotically normal, and easy to implement. This estimator overcomes a difficulty in maximum likelihood estimation: both the full and composite likelihoods are unbounded when the kernel distribution is normal. Our simulation studies show that the new estimator is highly efficient and robust. We apply the method to a time series for the USD/GBP exchange rate under a two-state hidden Markov model, as suggested by Engel and Hamilton (1990). The composite likelihood approach is more robust for inference than the full likelihood.

Key words and phrases: α-mixing, EM-algorithm, equilibrium distribution, ergodicity, finite mixture model, forward-backward algorithm, regime-switching, regularization, stationary.