Testing for a unit root in a nonlinear quantile autoregression framework

The nonlinear unit root test of Kapetanios, Shin, and Snell (2003 Kapetanios, G., Shin, Y., Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112:359–379.Crossref], Web of Science ®] , Google Scholar]) (KSS) has attracted much recent attention. However, the KSS test relies on the ordinary least squares (OLS) estimator, which is not robust to a heavy-tailed distribution and, in practice, the test suffers from a large power loss. This study develops three kinds of quantile nonlinear unit root tests: the quantile t-ratio test; the quantile Kolmogorov–Smirnov test; and the quantile Cramer–von Mises test. A Monte Carlo simulation shows that these tests have significantly better power when an innovation follows a non-normal distribution. In addition, the quantile t-ratio test can reveal the heterogeneity of the asymmetric dynamics in a time series. In our empirical studies, we investigate the unit root properties of U.S. macroeconomic time series and the real effective exchange rates for 61 countries. The results show that our proposed tests reject the unit roots more often, indicating that the series are likely to be asymmetric nonlinear reverting processes.