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Title: Monte Carlo likelihood ratio tests for Markov switching models Authors:  Gabriel Rodriguez Rondon - McGill University (Canada) [presenting]
Jean-Marie Dufour - McGill University (Canada)
Abstract: Markov switching models have wide applications in economics, finance, and other fields. Many studies focusing on identifying the number of regimes in a Markov switching model have been limited to hypothesis tests with a null of one regime and an alternative hypothesis of two regimes. We use Monte Carlo procedures to deal with nuisance parameters and circumvent the issues plaguing conventional hypothesis testing procedures by working with the sample distribution of the test statistic. The tests proposed here can deal with non-stationary processes, non-Gaussian errors, and multivariate settings. They are also applicable to the general setting where we are interested in testing a null hypothesis with $M_0$ regimes against an alternative with $M_0+m$ regimes where both $M_0, m \geq 1$. Further, the maximized Monte Carlo likelihood proposed ratio test (MMC-LRT) is an identifications-robust, valid test procedure both in finite samples and asymptotically. Simulation results are provided for both univariate and multivariate settings and suggest the proposed tests can control the level of the test and have good power. Finally, we present an empirical application using U.S. GNP growth data to showcase the usefulness of our proposed test procedures.