The components of empirical multifractality in financial returns

By Wei‐Xing Zhou. 2009

183 citations recorded by the source corpus.

We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with those of four kinds of surrogate data: 1) shuffled data that contain no temporal correlation but have the same distribution, 2) surrogate data in which any nonlinear correlation is removed but the distribution and linear correlation are preserved, 3) surrogate data in which large positive and negative returns are replaced with small values, and 4) surrogate data generated from alternative fat-tailed distributions with the temporal correlation preserved. We find that all these factors have influence on the multifractal spectrum. We also find that the temporal structure (linear or nonlinear) has minor impact on the singularity width Δα of the multifractal spectrum while the fat tails have major impact on Δα, which confirms the earlier results. In addition, the linear correlation is found to have only a horizontal translation effect on the multifractal spectrum in which the distance is approximately equal to the difference between its DFA scaling exponent and 0.5. Our method can also be applied to other financial or physical variables and other multifractal formalisms.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ce5fe688c74a246d57ef215d8b61b7b2eaf22b75

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Citations in the corpus

Multifractal detrended cross-correlations between the Chinese exchange market and stock market (2012, background): “Besides, for the limited size of the sample, we have to admit that there may be a finite-size effect in the determination of the scaling exponents [46,47] in our empirical analysis.”
Finite-size effect and the components of multifractality in financial volatility (2009, methodology): “Reference [60] shows that the multifractal spectrum width DaSF of the shuffled data is comparable to the apparent singularity width Da, which means that the long-term correlations have minor impact on Da and the fat-tailed PDF plays a major role.”
Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA (2013, methodology): “[42] to generate the surrogate data with Gaussian distribution while maintaining the linear correlation of the original data [43,44].”