Testing for a Linear Unit Root against Nonlinear Threshold Stationarity

In this paper we propose a direct testing procedure to detect the presence of linear unit root against geometrically ergodic process defined by the self-exciting threshold autoregressive (SETAR) model with three regimes. Assuming that the process follows the random walk in the corridor regime, the null can be tested by the Wald test for the joint significance of the threshold autoregressive parameters under both lower and upper regimes. We prove that the suggested Wald test does not depend on unknown threshold values under the null at least asymptotically. We also derive its analytic asymptotic null distribution. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the standard Dickey-Fuller test that ignores the threshold nature under the alternative.