Unit Root Testing with Stationary Covariates in the Framework of Asymmetric STAR Nonlinearity

Abstract

This paper generalizes the univariate unit root test proposed by Sollis (2009) by adding correlated covariates for a power boost. The asymptotic distribution of the proposed test is derived, and the asymptotic critical values are tabulated. Simulation experiments are conducted to demonstrate that for both small and moderate sample sizes found in applications, the new test can exhibit an excellent control over the empirical sizes, and most importantly, it delivers larger power gains from inclusion of correlated covariates, as compared to the counterpart without covariates. An application to real exchange rates for 18 Asian countries suggests that our proposed test is able to unveil stronger evidence in favour of mean reversion in real exchange rates than the counterpart without covariates does. Moreover, several real exchange rates are tested to display asymmetries in the adjustment process towards their equilibrium values.