MIRROR-IMAGE DISTRIBUTIONS AND THE DICKEY-FULLER REGRESSION WITH A MAINTAINED TREND

A puzzle of many empirical studies where Dickey-Fuller regressions wit h a maintained trend are run, is that the t-test of the AR-root and th e trend t-statistic frequently appear to be of equal magnitude but wit h opposite sign. In this paper I demonstrate that when the true proces s contains a drift, then the asymptotic distributions of the two stati stics will be the mirror image of each other and even in finite sample s this property will be predominant as long as the standardized drift is sufficiently strong.