Testing for stationarity with covariates: more powerful tests with non-normal errors

Previous studies suggested that the power of unit root and stationarity tests can be improved by augmenting a testing regression model with stationary covariates. However, one practical problem arises since such procedures require finding the variables that satisfy certain conditions. The difficulty of finding satisfactory covariate has hindered using such desired tests. In this paper, we suggest using non-normal errors to construct stationary covariates in testing for stationarity. We do not need to look for outside variables, but we utilize the distributional information embodied in a time series of interest. The terms driven from the information on non-normal errors can be employed as valid stationary covariates. For this, we adopt the framework of stationarity tests of Jansson (Jansson, M. 2004. “Stationarity Testing with Covariates.” Econometric Theory 20: 56–94). We show that the tests can achieve much-improved power. We then present the response surface function estimates to facilitate computing the critical values and the corresponding p-values. We investigate the nature of shocks to the US macro-economic series using the updated Nelson–Plosser data set through our new testing procedure. We find stronger evidence of non-stationarity than their univariate counterparts that do not use the covariates.