A SIMPLE MULTIPLE VARIANCE RATIO TEST

Empirical applications of the variance ratio (VR) test frequently empl oy multiple VR estimates to examine the random walk hypothesis against stationary alternatives. Failing to control the joint test size for t hese estimates results in very large Type I errors. This manuscript ex tends the Lo and MacKinlay (1988) methodology and provides a simple mo dification for testing multiple variance ratios. Monte Carlo results i ndicate that the size of our test is close to its nominal size and tha t 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 i s comparable to both the D-F and the P-P tests and seems to be more po werful than these tests against two unit root alternatives, an ARIMA(1 ,1,1) and an ARIMA(1,1,0).