Computation of Restricted Maximum-penalized-likelihood Estimates in Hidden Markov Models

The maximum-penalized-likelihood estimation for hidden Markov models with general observation densities is described. All statistical inference, including the model estimation, testing, and selection, is based on the restricted optimization of the penalized likelihood function with respect to the chosen model family. The method is used in an economic application, where stock market index returns are modeled with hidden Markov models. Special emphasis is placed on modeling isolated outliers in the data, which has usually been ignored in previous research. The chosen model ts the data well, and is capable of modeling the outliers as well as a structural change in the series.