Testing linearity against smooth transition autoregression using a parametric bootstrap

When testing the null hypothesis of linearity of a univariate time series against smooth transition autoregression (STAR), standard asymptotic distribution results do not apply since nuisance parameters in the model are unidentified under the null hypothesis. The prevailing test of Luukkonen, Saikkonen and Teräsvirta (1988) is based on a linearization, which may adversely affect its power. This paper discusses an alternative procedure, based on a parametric bootstrap of a likelihood ratio test statistic, and investigates its size and power properties by a small simulation study. The results, however, indicate that the power of the bootstrap test is inferior to that of the existing test.