Power issues when testing the Markov switching model with the sup likelihood ratio test using U.S. output

The likelihood ratio (LR) test statistic for the test of a linear AR(1) model against the alternative of a Markov switching model does not possess the standard 2 distribution. Garcia (1998) derives the asymptotic distribution of the Sup LR test statistic under these non-standard conditions allowing the researcher to easily compare the two models. This paper examines the power properties of this test statistic using Monte Carlo experiments calibrated to U.S. output growth data. The results suggest a test of reasonable power. When the experiments are calibrated to annual data, power is 82% at 200 observations. When the experiments are calibrated to quarterly data power is 57% for the same sample size.