ABSTRACT
The Smooth Transition Autoregressive (STAR) model is one of the most widely used non-linear time series models, in which the Logistic Smooth Transition Autoregressive (LSTAR) model is a an important form. The STAR modeling is a challenging job, and linear test is a necessary step for the STAR modeling. In the earlier literature, many scholars assume that the series is stationary before STAR modeling (Luukkonen, 1988; Teräsvirta, 1994). Recently, some scholars recognize that the statistic of the linear test is non-standard, so that people should implement unit root test before linear test for the STAR models (Kapetanios et al., 2003; Kilic, 2004; Sandberg, 2008). However, the unit root tests which are proposed by them are either linear test or detached from the linear test. This paper proposes a new notion of unit root test for LSTAR model which is run in the nonlinear LSTAR model’s third-order Taylor expansion where the linear test can also be done at the same time.
