Identication-robust moment-based tests for Markov switching in autoregressive models

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identi!cation failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model speci!cation. The proposed tests have very respectable power in comparison with the optimal tests for Markov-switching parameters of Carrasco et al. (2014), and they are also quite attractive owing to their computational simplicity. The new tests are illustrated with an empirical application to an autoregressive model of USA output growth