The size performance of a nonparametric unit root test under a variance shift

This paper examines the size performance of Breitung's [2002. Nonparametric tests for unit roots and cointegration. J. Econometrics 108, 343-363.] nonparametric unit root test in the presence of a variance shift. We show that the limiting distribution of the test statistic in the presence of a variance shift depends on the break point of the variance and the ratio of the prebreak to the postbreak variance, as in the case of the standard Dickey-Fuller test. However, our Monte Carlo simulations provide clear evidence that Breitung's nonparametric unit root test achieves a far superior size performance as compared with the Dickey-Fuller test.