02046cam a22002417 4500001000600000003000500006005001700011008004100028100001800069245015800087260006600245490005100311500001500362520103200377530006101409538007201470538003601542700002501578710004201603830008601645856003701731856003601768t0066NBER20170925111337.0170925s1988 mau||||fs|||| 000 0 eng d1 aLo, Andrew W.14aThe Size and Power of the Variance Ratio Test in Finite Samplesh[electronic resource]:bA Monte Carlo Investigation /cAndrew W. Lo, A. Craig MacKinlay. aCambridge, Mass.bNational Bureau of Economic Researchc1988.1 aNBER technical working paper seriesvno. t0066 aJune 1988.3 aWe 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 hypothesis of a random walk with independent and identically distributed Gaussian increments, the empirical size of all three tests are comparable. Under a heteroscedastic 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.1 aMacKinlay, A. Craig.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0066.4 uhttp://www.nber.org/papers/t006641uhttp://dx.doi.org/10.3386/t0066