Another Look At Long Memory In Common Stock Returns

We apply Lo's (Econometrica, 1991, 59, 1279-1313) modified R/S test to the returns series of 1,952 ordinary common stocks. We use asymptotic and bootstrapped critical values to evaluate the significance of the test statistics, which are computed for several different fixed and sample-size dependent autocovariance lag-truncation lengths. In contrast to the findings of Greene and Fielitz (Journal of Financial Economics, 1977, 4, 339-349), the results of the application indicate that long memory is not a widespread phenomenon influencing the returns series of common stocks. We confirm this conclusion by testing for long memory using an alternative approach developed by Geweke and Porter-Hudak (Journal of Time Series Analysis, 1983, 4, 221-238). We also employ logit models to study the probability of a rejection of Lo's short-term dependence null by the modified R/S test. The results from our logit study indicate that the event of a rejection by the test is linked to short- lived firms which eventually merge, to firms in the communications, transportation, and utilities industries, and to firms which bear relatively little market risk. The maximal moment of a stock's return distribution is also found to influence the event of a rejection. Some of the results from our logit study lend empirical support to the theoretical work of Brown, Goetzmann, and Ross (unpublished manuscript, 1993, Graduate School of Business, Columbia University) who show that the rescaled range test is sensitive to survivorship bias.