A Penalized Quasi-Likelihood Approach for Estimating the Number of States in a Hidden Markov Model

• Activity Number: 323
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Annaliza McGillivray*+ and Abbas Khalili
• Companies: McGill University and McGill University
• Keywords: hidden Markov model ; penalized likelihood ; mixture model

Abstract

In statistical applications of hidden Markov models (HMMs), one may have no knowledge of the number of hidden states (or order) of the model needed to be able to accurately represent the underlying process of the data. The problem of estimating the number of hidden states of the HMM is thus brought to the forefront. In this talk, we present a penalized quasi-likelihood approach for order estimation in HMMs which makes use of the fact that the marginal distribution of the observations from a HMM is a finite mixture model. The method starts with a HMM with a large number of states and obtains a model with lower order by clustering and combining similar states of the model through two penalty functions. We assess the performance of the new method theoretically and via extensive simulation studies for Normal and Poisson HMMs as well as with an application to a real data set.