Empirical asset return distributions: Is chaos the culprit?

Abstract

This study employs Rescaled-range analysis; the Correlation Dimension test, and the BDS test, to analyse lengthy daily time series of financial data. Two equity and two commodity indices are examined. The results reject the hypothesis that the series are purely random, independent and identically distributed. Rather, they suggest consistency with the Pareto-Levy family of processes. Motivated by the capacity of certain chaotic models to generate data consistent with these processes, evidence is accumulated consistent with a strange attractor, a long-term memory effect, and a-periodic motion. The evidence is consistent with insights derived from the theory of non-linear dynamics.