Another look at long memory in common stock returns

We apply the modified rescaled range test to the return series of 1,952 common stocks. The results indicate that long memory is not a widespread characteristic of these stocks. But logit models of the event of a test rejection reveal that rejections are linked to firms with large risk-adjusted average returns. The maximal moment of a return distribution is also found to influence the event of a rejection, but not in a way suggestive of moment-condition failure. Evidence suggestive of survivorship bias is also uncovered. We conclude that there is some evidence consistent with persistent long memory in the returns of a small proportion of stocks.