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.