Optimal Test for Markov Switching
نویسندگان
چکیده
The aim of the paper is to propose an optimal test for the null hypothesis of parameter constancy H0 : θt = θ0 against an alternative where the parameters vary according to an unobservable Markov chain. This testing problem includes testing the parameter stability in a Markov-switching model (Hamilton, 1989) and in a random coefficient model (for example a state space model). The model under the null need not be linear, it may be a GARCH model for instance. The parameters driving the dynamic of the underlying Markov chain are not identiÞed under the null hypothesis. As a result, the testing problem is non-standard and the likelihood ratio test does not converge to a chi-square distribution. Our test is based on functionals of expressions like
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