Nonparametric Inference and Order Selection in Hidden Markov Models

Hidden Markov models (HMMs) and their various extensions have been successfully applied in various disciplines, including biology, speech recognition, economics/finance, climatology, psychology and medicine. They combine immense flexibility with relative mathematical simplicity and computational tractability, and as a consequence have become increasingly popular as general-purpose models for time series data. In this talk, I will first introduce the basic HMM machinery, illustrating the key concepts and tools using real-data applications. I will then demonstrate how the HMM machinery can be combined with penalised splines to allow for flexible nonparametric inference in HMM-type classes of models. This will lead us to a discussion on how to select an adequate number of states, and eventually also to the choice to be made on whether to use discrete or continuous state processes.