Statistical Properties of a Time-Series-Complexity Measure Applied to Stock Returns.

We review a complexity measure theta and its statistical properties, then apply it to four stock returns. Theta is a ratio of two correlation integral estimates, one taken before and one after shuffling the series to investigate. For random processes theta approximate 1 while theta approaches zero for data with low complexity. Sixteen artificially generated series with different dynamical characteristics--each represented by three sample sizes--were employed to investigate theta's statistical properties. Its distribution approaches normality as the sample size is increased. When applied to stock returns, those computed at every price change proved less complex than lower frequency one- and five-minute returns, implying that information is being lost by increasingly less frequent sampling. Citation Copyright 1998 by Kluwer Academic Publishers.