In tbis article we test the random walk bypotbesis for weekly stock market returns by comparing vari-ance estimators derived. from data sampled at dif-ferent frequencies. Tbe random walk model is strongly rejectedfor tbe entire sample period (1962-1985) and for all subperiods for a variety of aggre-gate returns indexes and size-sorted portfolios.Altbougb tbe rejections are due largely to tbe bebav-ior of small stocks, tbey cannot be attributed com-pletely to tbe effects of infrequent trading or time-varying volatilities. Moreover, tbe rejection of tbe random walk. for weekly returns does not support a mean-reverting model of asset prices.