Optimal Test for Markov Switching Parameters

This paper proposes a class of optimal tests for the constancy of parameters in random coe ¢ cients models. Our testing procedure covers the class of Hamiltons models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coe ¢ cients need not be Markov. Standard approaches do not apply. We use Bartlett-type identities for the construction of the test statistics. It has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, we show that the tests of this class are asymptotically optimal in the sense that they maximize a weighted power function. Moreover, we show that the contiguous alternatives converge to the null with a nonstandard rate of decay