Finite-size effect and the components of multifractality in financial volatility
By Wei‐Xing Zhou. 2009
138 citations recorded by the source corpus.
Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.
Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0630fc007e4ef5a60403a608fab51da9a7b74885
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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.”
- Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA (2013, background): “[56,57] show that a finite-size effect in our empirical analysis may be present, and additional data are needed to obtain reliable results because a window length of 5000, which is the length of the time series in our study, is not short.”