Variance-ratio Tests Robust to a Break in Drift (European Journal of Pure and Applied Mathematics, 2010)
We consider a simple random walk process which exhibits a deterministic break in its drift term: for instance, from positive to negative. We demonstrate both theoretically and by simulation that when the standard variance ratio test is applied to this process, the phenomenon of spurious rejections of the random walk hypothesis can occur. We further propose a modi fied version of the variance ratio test to avoid such a problem. Finally, we discuss some implications of this finding on the previously revealed empirical evidence against the random walk hypothesis for exchange rates.