Self-similarity and multifractality in financial asset returns

Abstract

This paper presents an empirical investigation of scaling and the multifractal properties of financial asset returns. It discusses the key intuition relative to the applicability of scaling processes and the broader class of multifractal processes to financial phenomena. The cumulative return distribution of positive and negative tails at the different time intervals are linear. This presents strong evidence that returns exhibit power-law scaling in the tails. To test the multifractal properties of returns, we use the sample absolute moment of the aggregated return series. These moments do not scale linearly with different lags. In the other words, the scaling exponent is nonlinear in lags. These results indicate that the returns are multifractal.