Testing for observation-dependent regime switching in mixture autoregressive models

Testing for regime switching when the probabilities are specified either as constants (‘mixture models’) or governed by a finite-state Markov chain (‘Markov long-standing problems that have also attracted recent interest. This paper considers testing time-varying and depend on observed data (‘observation-dependent switching’). Specifically, we consider likelihood ratio test observation-dependent in mixture autoregressive models. The problem is highly nonstandard, involving unidentified nuisance parameters under null, boundary, singular information matrices, higher-order approximations of log-likelihood. We derive asymptotic null distribution statistic general setting using high-level conditions allow various forms dependence past observations, illustrate theory two particular has nonstandard can easily be simulated, Monte Carlo studies show to good finite sample size power properties.