Multifractal detrended fluctuation analysis: Practical applications to financial time series

James R. Thompson and James R. Wilson

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 126, issue C, 63-88

Abstract: 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.

Keywords: Financial time series; Multifractal process; Multifractal detrended fluctuation analysis; Multifractal spectrum; Self-similar process (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:126:y:2016:i:c:p:63-88

DOI: 10.1016/j.matcom.2016.03.003

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