Test of ibe Random walk Individual securities results for a one- week base observation period lumber g of base observations aggregated ng of b form variance ratio Averages of variance ratios over individual securities 625 stocks) (0.08) (0 03 (100 stocks, (0.13) (100 stocks) Variance ratios of equal- and value-weighted portfolios of all stocks 1216 ith complete return histories from September 2, 62, to December 26, 1985(625 stocks) ariance ratios for the smallest 100 stocks, the inte t cross-sectionally independent, the sta annot be used to perform the usual significance tests; they are rep (panel B) re the heteroscedasticity-robust z(q) statistics. Asterisks indicate variance ratios tha nat are statistical different from I at the 5 percent level of significance random walk hypothesis for the logarithm of wealth relatives of small-firms portfolios is strong in all cases considered. For larger firms and a one-week base observation interval the evidence is also inconsistent with the random walk: however, as the base observation interval is increased to four weeks our test does not reject the random walk model for larger firms 2.3 Results for individual securities For completeness, we performed the variance-ratio test on all individual stocks that have complete return histories in the crsP database for our entire 1216-week sample period, yielding a sample of 625 securities. Owing to space limitations, we report only a brief summary of these results in Table 3. Panel A contains the cross-sectional means of variance ratios for the entire sample as well as for the 100 smallest, 100 intermediate, and 100 largest stocks. Cross-sectional standard deviations are given in paren theses below the main rows. Since the variance ratios are clearly not cross sectionally independent, these standard deviations cannot be used to form the usual tests of significance; they are reported only to provide some indication of the cross-sectional dispersion of the variance ratios The average variance ratio for individual securities is less the when q=2, implying that there is negative serial correlation on av