Exact Non-Parametric Tests for a Random Walk with Unknown Drift under Conditional Heteroscedasticity

This paper proposes a class of linear signed rank statistics to test for a random walk with unknown drift in the presence of arbitrary forms of conditional heteroscedasticity. The class considered includes analogues of the well-known sign and Wilcoxon test statistics. The exactness of the proposed tests rests only on the assumption that the errors are symmetrically distributed. No other assumptions, such as normality or even the existence of moments, are required. Simulations confirm the reliability of the proposed tests, and their power is superior to that of the parametric variance-ratio test. The inference methods developed are illustrated by a test of the random walk hypothesis in exchange rates for five major currencies against the U.S. dollar.