2016 journal article

Multifractal detrended fluctuation analysis: Practical applications to financial time series

MATHEMATICS AND COMPUTERS IN SIMULATION, 126, 63–88.

co-author countries: United States of America 🇺🇸
author keywords: Financial time series; Multifractal process; Multifractal detrended fluctuation analysis; Multifractal spectrum; Self-similar process
Source: Web Of Science
Added: August 6, 2018

To analyze financial time series exhibiting volatility clustering or other highly irregular behavior, we exploit multifractal detrended fluctuation analysis (MF-DFA). We summarize the use of local Hölder exponents, generalized Hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit light- or heavy-tailed fluctuations as well as short- or long-range dependence on different time scales. We detail the development of a robust, computationally efficient software tool for estimating the multifractal spectrum from a time series using MF-DFA, with special emphasis on selecting the algorithm’s parameters. The software is tested on simulated sample paths of Brownian motion, fractional Brownian motion, and the binomial multiplicative process to verify the accuracy of the resulting multifractal spectrum estimates. We also perform an in-depth analysis of General Electric’s stock price using conventional time series models, and we contrast the results with those obtained using MF-DFA.