THE SIZE AND POWER OF THE VARIANCE RATIO TEST IN FINITE SAMPLES: A MONTE CARLO INVESTIGATION

*Journal of Econometrics* 40(1989), 203–238.

Andrew W. Lo and A. Craig MacKinlay

We examine the finite-sample properties of the variance ratio test of the
random walk hypothesis via Monte Carlo simulations under two null and three
alternative hypotheses. These results are compared to the performance of the
Dickey-Fuller *t* and the Box-Pierce *Q* statistics. Under the
null hypotheses of a random walk with independent and identically distributed
Gaussian increments, the empirical size of all three tests are comparable.
Under the heteroskedastic random walk null, the variance ratio test is more
reliable than either the Dickey-Fuller or Box-Pierce tests. We compute the
power of these three tests against three alternatives of recent empirical
interest: a stationary AR(1), the sum of this AR(1) and a random walk, and an
integrated AR(1). By choosing the sampling frequency appropriately, the
variance ratio test is shown to be as powerful as the Dickey-Fuller and
Box-Pierce tests against the stationary alternative and is more powerful than
either of the two tests against the two unit root alternatives.