A Family of Likelihood Ratio-Based Tests for Markov Regime Switching

• Activity Number: 626
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Zhongjun Qu and Fan Zhuo*+
• Companies: Boston University and Boston University
• Keywords: Hypothesis testing ; likelihood ratio ; Markov switching

Abstract

This paper studies a family of tests for the presence of Markov regime switching in linear time series models. The framework allows the regime switching to affect only a subset or all of the regression coefficients. The tests are based on empirical processes of likelihood ratio statistics. They explicitly exploit serial dependence properties implied by the Markov structure. The analysis addresses three challenges, i.e., unidentified nuisance parameters under the null hypothesis, identical zero scores and the stochastic nature of the conditional transition probability. Addressing the third challenge is crucial as it provides a channel for asymptotic pivotality and also leads to tests with higher power against some alternatives than those existing in the literature. In the process, the paper makes three technical contributions: (1) a characterization of the dynamics of the conditional transition probability, (2) an approximation to the log-likelihood ratio test statistics to the fourth order, and (3) a general formula for the limiting distribution allowing for multiple switching parameters. The tests are illustrated through Monte Carlo experiments and an empirical example.