Test for linearity against STAR models with deterministic trends

This paper studies the linearity test of STAR models with deterministic trends. The results show that when the data generation process includes a deterministic trend, the Wald-type statistic proposed by Teräsvirta (1994) does not follow the standard χ2 distribution, but degenerates at the speed of T. Moreover, when the test for linearity is performed based on the residual of ordinary least squares detrending, the statistical power of the test is very low even when the Wald statistic follows the χ2 distribution.