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Home | Events | Testing for Observation-dependent Regime Switchingin Mixture Autoregressive Models

Testing for Observation-dependent Regime Switchingin Mixture Autoregressive Models

  • Location
    Tinbergen Institute (Gustav Mahlerplein 117)
  • Date and time

    October 23, 2020
    16:00 - 17:15

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

JEL classification:C12, C22, C52.

Keywords:Likelihood ratio test, singular information matrix, higher-order approximation of thelog-likelihood, logistic mixture autoregressive model, Gaussian mixture autoregressive model