Unit root quantile autoregression testing using covariates

This paper extends unit root tests based on quantile regression proposed by Koenker and Xiao [Koenker, R., Xiao, Z., 2004. Unit root quantile autoregression inference, Journal of the American Statistical Association 99, 775–787] to allow stationary covariates and a linear time trend. The limiting distribution of the test is a convex combination of Dickey–Fuller and standard normal distributions, with weight determined by the correlation between the equation error and the regression covariates. A simulation experiment is described, illustrating the finite sample performance of the unit root test for several types of distributions. The test based on quantile autoregression turns out to be especially advantageous when innovations are heavy-tailed. An application to the CPI-based real exchange rates using four different countries suggests that real exchange rates are not constant unit root processes.