Unit Root Testing in Presence of a Double Threshold Process

In this paper we propose a double threshold process that generalizes the threshold autoregressive one widely known in the literature. It is characterized by a structure with two thresholds: the first regulates the switching between two autoregressive regimes; the second threshold regulates the switching between the two regimes of the stationary innovations. A testing procedure based on a Wald statistic has been given to evaluate the presence of unit roots in the process against stationarity. The asymptotic distribution of the statistic has been derived and the size and the power of the test have been evaluated through a Monte Carlo study where the proposed test is compared to two competing unit root testing procedures. The results clearly highlight the advantage obtained from the proposed test as the asymmetry of the generating process increases.