Is it possible to discriminate between different switching regressions models? An empirical investigation

In this paper we study, using the sup LR test, the possibility of discrimination between two classes of models: the Markov switching models of Hamilton (1989) and the Threshold Auto-Regressive Models (TAR) of Lim and Tong (1980). This work is motivated by the fact that generally practicians use, in applications, switching models without any statistical justification. Using experiment simulations, we show that it is very difficult to discriminate between the MSAR and the SETAR models specially using large samples. This means that when the null hypothesis is rejected, it appears that different switching models are significant. Moreover, the results show that the power of the sup LR test is sensitive to the mean, the noise variance and the delay parameter. Then, we apply this methodology to two time series: the US GNP growth rate and the US/UK exchange rate. We shall retain retain a Markov switching process for the US GNP growth rate and the US/UK exchange rate (monthly data). For the US/UK exchange rate (quarterly data), we accept the null hypothesis of a random walk.