Inference and Application of Likelihood Based Methods for Hidden Markov Models

The thesis consists of three papers. In the paper “Testing for the number of states in hidden Markov models” we generalize existing testing procedures for i.i.d. mixture models to hidden Markov models by considering penalized quasi-likelihood ratio tests. They can be applied in order to assess the number of states k of a hidden Markov model with univariate state-dependent distribution fulfilling certain regularity conditions. In the paper “Hidden Markov Models with state-dependent mixtures” we analyze the dependence structure of hidden Markov models with state-dependent finite mixtures. Our results have applications to model selection as well as to model-based clustering. We propose algorithms for both purposes. In the paper “Peaks vs Components” we analyze welfare groups of countries all over the world by applying finite mixture models to the GDP per capita of 190 countries from 1970 to 2009