Long-term memory in equity style indexes

The widely accepted mean-reverting model of stock returns identified in several studies is included in the broader class of long-term memory statistical time series models. A common alternative to the long-term memory model is the random walk model. Consistent with recent research using variance ratio tests, the author finds chat the random walk model cannot be rejected for monthly returns on broad market indexes. A finding is that the random walk model also cannot be rejected for major equity style indexes and indexes representing style index return differentials. The results presented here suggest that if equity index returns are to be predictable, they must be conditioned on outside information.