Multifractal detrended fluctuation analysis: Practical applications to financial time series

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• 作者：James R. Thompson^a ; James R. Wilson^b ; ^{jwilson@ncsu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Financial time series ; Multifractal process ; Multifractal detrended fluctuation analysis ; Multifractal spectrum ; Self-similar process
• 刊名：Mathematics and Computers in Simulation
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：126
• 期：Complete
• 页码：63-88
• 全文大小：3648 K

文摘

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.