Testing linearity against smooth transition autoregressive models

Abstract

We study a general univariate smooth transition autoregressive, star, model. It contains as a special case the self-exciting threshold autoregressive, setar, model. We present three tests for testing linearity against star models and discuss their properties. The power of the tests in small samples is investigated by simulation when the alternative is the logistic star model. One of the tests is identical to Tsay's (1986) test statistic and is recommended only in a special case. Of the two remaining tests with wider applicability, one seems superior to the other in small samples. It is also more powerful than the cusum test recently proposed for testing linearity against setar models.