Markov Regime-Switching Tests: Asymptotic Critical Values

Empirical research with Markov regime-switching models often requires the researcher not only to estimate the model but also to test for the presence of more than one regime. Despite the need for both estimation and testing, methods of estimation are better understood than are methods of testing. We bridge this gap by explaining, in detail, how to apply the newest results in the theory of regime testing, developed by Cho and White (2007). A key insight in Cho and White is to expand the null region to guard against false rejection of the null hypothesis due to a small group of extremal values. Because the resulting asymptotic null distribution is a function of a Gaussian process, the critical values are not obtained from a closed-form distribution such as the . Moreover, the critical values depend on the covariance of the Gaussian process and so depend both on the speci…cation of the model and the speci…cation of the parameter space. To ease the task of calculating critical values, we describe the limit theory and detail how the covariance of the Gaussian process is linked to the speci…cation of both the model and the parameter space. Further, we show that for linear models with Gaussian errors, the relevant parameter space governs a standardized index of regime separation, so one need only refer to the tabulated critical values we present. JEL Classi…cation: Primary C15; Secondary C12