Detrended cross-correlation analysis consistently extended to multifractality

Paweł Oświȩcimka, Stanisław Drożdż, Marcin Forczek, Stanisław Jadach, and Jarosław Kwapień
Phys. Rev. E 89, 023305 – Published 21 February 2014

Abstract

We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter λq. This relation provides information about the character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.

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  • Received 28 August 2013
  • Revised 26 November 2013

DOI:https://doi.org/10.1103/PhysRevE.89.023305

©2014 American Physical Society

Authors & Affiliations

Paweł Oświȩcimka1,*, Stanisław Drożdż1,2, Marcin Forczek1, Stanisław Jadach1, and Jarosław Kwapień1

  • 1Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland
  • 2Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, PL 31-155 Kraków, Poland

  • *pawel.oswiecimka@ifj.edu.pl

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Vol. 89, Iss. 2 — February 2014

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