Testing for Linearity in Markov Switching Models: A Bootstrap Approach.

Testing for linearity in the context of Markov switching models is complicated because standard regularity conditions for likelihood based inference are violated. This is due to the fact that, under the null hypothesis of linearity, some parameters are not identified and scores are identically zero. Thus the asymptotic distribution of the test statistic of interest does not possess the standard χ2-distribution. In this paper we propose a bootstrap resampling scheme to approximate the distribution of the test statistic of interest under the null of linearity. The procedure is relatively easy to program and the computation requirements are reasonable. We investigate the performance of the bootstrap-based test using Monte Carlo simulations. We find that the test works well and outperforms the Hansen test and the Carrasco et al. test. The use of the various methods is also illustrated by means of empirical examples.