Test of tbe Random walk of some economic model of efficient price formation, there may exist other plausible models that are consistent with the empirical findings. Our more modest goal in this study is to employ a test that is capable of distinguishing among several interesting alternative stochastic price processes. Our test exploits the fact that the variance of the increments of a random walk is linear in the sampling interval. If stock prices are generated by a rando walk (possibly with drift), then, for example, the variance of monthly sampled log-price relatives must be 4 times as large as the variance of a weekly sample. Comparing the(per unit time) variance estimates obtained from weekly and monthly prices may then indicate the plausibility of the random walk theory. 2 Such a comparison is formed quantitatively along he lines of the Hausman(1978) specification test and is particularly simple In Section 1 we derive our specification test for both homoscedastic and heteroscedastic random walks. Our main results are given in Section 2 where rejections of the random walk are extensively documented for weekly returns indexes, size-sorted portfolios, and individual securities Section 3 contains a simple model which demonstrates that infrequent trading cannot fully account for the magnitude of the estimated autocorrelations of weekly stock returns. In Section 4 we discuss the consistency of our empirical rejections with a mean. reverting alternative to the random walk model We summarize briefly and conclude in Section 5 =和 o not provide any formal samplin Campbell and Mankiw(1987) and Cochrane(1987b)do derive the asymptotic more ce of der the nui Our variance ratio may, however, be related to the spectral-density estimates in the following fo) denote the spectral density of the increments AX, at frequency 0, we have the following relation x/(0)=1(0)+2∑?(k) where y(k)is the autocovariance function Dividing both sides by the variance y(o) then yields r"(0)=1+2∑p(k where. is the n ity and p(k) is the autocorrelation n Now sum on the right-hand side of the preceding equation m use this variance ratio, Huizinga (1987) does employ the Newey and West(1987) estimator of the normalized spectral densi