Understanding the source of multifractality in financial markets

TL;DR

This study investigates the multifractal nature of financial markets using the generalized Hurst exponent, revealing that fat-tailed distributions primarily drive multifractality, while correlations tend to reduce it.

Contribution

It demonstrates the robustness of the generalized Hurst exponent approach and uncovers the counterintuitive increase of multifractality in shuffled data, attributing it mainly to fat-tailed distributions.

Findings

Multifractality is mainly due to fat-tailed return distributions.

Time correlations tend to decrease measured multifractality.

Shuffled data can show increased multifractality due to distribution effects.

Abstract

In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal (MSM) model, autoregressive fractionally integrated moving average (ARFIMA) processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality.