Penalized likelihood based tests for regime switching in autoregressive models

In this thesis, we are mainly concerned with the basic methodological issue to test for regime switching in various Markov-switching autoregressive models. To this end, we develop some penalized likelihood based tests which neglect the dependence structure in the latent process. We derive the asymptotic distribution of the corresponding test statistics under the hypothesis. Finally, we apply our methods to financial and macroeconomic time series