An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models

The unit root tests of Caner and Hansen (Econometrica 69 (2001) 1555) for asymmetric time series models based on the ordinary least squares estimator (OLSE) have asymptotic null distributions that depend on parameters of asymmetry. We resolve this parameter dependency by adopting the instrumental variable estimation of Shin and Lee (J. Business & Economic Statist. 19 (2001) 233) and the recursive mean adjustment of Shin and So (J. Time Series Anal. 22 (2001b) 595). If the threshold parameter is known, the limiting null distribution of the proposed Wald test does not depend on any nuisance parameter and is chi-squared. If the threshold parameter is unknown and is estimated from data, then under threshold effect, the limiting null distributions of the proposed Wald tests are chi-squared as those for model with known threshold parameter whereas, under no threshold effect, they are chi-squared only conditionally on the weak limit of the estimated threshold parameter. Our Wald tests extend to seasonal models retaining the chi-square asymptotics regardless of the parameter of seasonality, which is not the case of the OLSE-based tests. Moreover, the proposed tests can be modified into one-sided Wald tests which are significantly more powerful than the tests of Caner and Hansen (2001). We apply our method to the monthly US unemployment rate and find some evidences of seasonal unit roots, suggesting nonstationarity rather than the strong stationarity of Caner and Hansen (2001).