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Detrended cross-correlation analysis consistently extended to multifractality.

Paweł Oświecimka1, Stanisław Drożdż2, Marcin Forczek1

  • 1Institute of Nuclear Physics, Polish Academy of Sciences, PL 31-342 Kraków, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
PubMed
Summary

We introduce multifractal cross-correlation analysis (MFCCA), a robust method to quantify complex cross-correlations in time series. MFCCA accurately identifies multifractality, overcoming limitations of existing techniques for analyzing natural and financial processes.

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Area of Science:

  • Complex Systems Analysis
  • Time Series Analysis
  • Statistical Physics

Background:

  • Existing methods for multifractal cross-correlation analysis have limitations in accurately quantifying subtle characteristics.
  • Many current techniques may incorrectly indicate multifractality in complex natural processes.

Purpose of the Study:

  • To introduce a novel algorithm, multifractal cross-correlation analysis (MFCCA), as a consistent extension of detrended cross-correlation analysis.
  • To accurately identify and quantify multifractal cross-correlations in time series data.
  • To provide a more reliable tool for analyzing complex natural and financial processes.

Main Methods:

  • Development of the multifractal cross-correlation analysis (MFCCA) algorithm.
  • Incorporation of the sign of fluctuations into generalized moments for improved accuracy.
  • Analysis of both model fractal stochastic processes and real-world signals, including stock market data.

Main Results:

  • MFCCA is demonstrated as a robust and selective tool for quantifying cross-correlative structures.
  • The algorithm accurately identifies multifractal scaling boundaries and the relationship between the generalized Hurst exponent and the multifractal scaling parameter λ(q).
  • Financial time series exhibit multifractal cross-correlations primarily for large fluctuations, with small fluctuations remaining independent.

Conclusions:

  • MFCCA offers a deeper insight into the dynamics of analyzed processes compared to existing methods.
  • The method enables reliable quantification of cross-correlative structures and potential multifractality.
  • MFCCA shows potential utility in studying time-lagged cross-correlations and analyzing financial market dynamics.