Understanding the source of multifractality in financial markets

• DOI: 10.1016/j.physa.2012.03.037
• Publication Date: 2012-04-13T19:37:27Z
• Authors: Jozef Barunik; Tomaso Aste; T. Di Matteo; Ruipeng Liu
• Keywords: Hurst exponent; Multifractal system; Fractional Brownian motion; Lévy flight

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.