A simple multiple variance ratio test

Abstract

Empirical applications of the variance ratio (VR) test frequently employ multiple VR estimates to examine the random walk hypothesis against stationary alternatives. Failing to control the joint test size for these estimates results in very large Type I errors. This manuscript extends the Lo and MacKinlay (1988) methodology and provides a simple modification for testing multiple variance ratios. Monte Carlo results indicate that the size of our test is close to its nominal size and that it is as reliable as the Dickey-Fuller (D-F) and the Phillips-Perron (P-P) unit root tests. For a stationary AR(1) alternative, our test is comparable to both the D-F and the P-P tests and seems to be more powerful than these tests against two unit root alternatives, an ARIMA(1,1,1) and an ARIMA(1,1,0).