REGIME-SWITCHING AUTOREGRESSIVE COEFFICIENTS AND THE ASYMPTOTICS FOR UNIT ROOT TESTS

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases+ Conversely, in this note we derive some new asymptotic results for the case of Markov regime switches that are infrequent in the sense that their number is bounded in probability, even asymptotically+ This is achieved by ~inversely! relating the probability of regime switching to the sample size+ The proposed asymptotic theory is applied to a wellknown stochastic unit root model, where the dynamics of the observed variable switches between a unit root regime and a stationary regime+