Can the SupLR test discriminate between different switching

In recent years two classes of switching models have been proposed, the Markov switching models, Hamilton (1989) and the Threshold Auto- Regressive Models (TAR), Lim and Tong (1980). These two models have the advantage of being able to modelize and capture asymmetry, sudden changes and irreversibility time observed in many economic and financial time series. Despite these similarities and common points, these models have been envolved, in the literature, largely independently. In this paper, using the $SupLR$ test, we study the possibility of discrimination between these two models. This approach is motivated by the fact that the majority of authors, in applications, use switching models without any statistical justification. We show that when the null hypothesis is rejected it appears that different switching models are significant. Then, using simulation experiments we show that it is very difficult to differenciate between MSAR and SETAR models specially with large samples. The power of the $SupLR$ test seems to be sensitive to the mean, the noise variance and the delay parameter which appear in each model. Finally, we apply this methodology to the US GNP growth rate and the US/UK exchange rate.