Homogeneity Test for Hidden Markov Models Using Penalized Composite Likelihood

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yi Huang*+ and Jiahua Chen
• Companies: and Universithy of British Columbia
• Keywords: Hidden Markov models ; Hypothesis testing ; Composite likelihood ; Penalized likelihood

Abstract

This presentation introduces a hypothesis testing methodology for the number of hidden states in hidden Markov models (HMMs). As a first step of our research project, we focus on testing the null hypothesis of one state against the alternative of two states in a HMM. This setting is nonstandard in the sense that parameters are on the boundary of the parameter space and they are identifiable only under the alternative. We exploit recent advances in finite mixtures and develop a test based on a composite likelihood, which considers the serial dependency of two successive observations only. A penalization technique is introduced to circumvent the nonstandard situation. The proposed test is computationally simple and has a handy asymptotic null distribution. Simulation studies indicate promising finite-sample performances of our proposed test in terms of size and power.