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Power-law cross-correlations: Issues, solutions and future challenges

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  • Ladislav Kristoufek

Abstract

Analysis of long-range dependence in financial time series was one of the initial steps of econophysics into the domain of mainstream finance and financial economics in the 1990s. Since then, many different financial series have been analyzed using the methods standardly used outside of finance to deliver some important stylized facts of the financial markets. In the late 2000s, these methods have started being generalized to bivariate settings so that the relationship between two series could be examined in more detail. It was then only a single step from bivariate long-range dependence towards scale-specific correlations and regressions as well as power-law coherency as a unique relationship between power-law correlated series. Such rapid development in the field has brought some issues and challenges that need further discussion and attention. We shortly review the development and historical steps from long-range dependence to bivariate generalizations and connected methods, focus on its technical aspects and discuss problematic parts and challenges for future directions in this specific subfield of econophysics.

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  • Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    • Handle: RePEc:arx:papers:1806.01616
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    References listed on IDEAS

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    1. Ladislav Kristoufek, 2014. "Spectrum-based estimators of the bivariate Hurst exponent," Papers 1408.6637, arXiv.org, revised Nov 2014.
    2. Rebecca J. Sela & Clifford M. Hurvich, 2012. "The averaged periodogram estimator for a power law in coherency," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 340-363, March.
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    15. Kristoufek, Ladislav, 2015. "Finite sample properties of power-law cross-correlations estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 513-525.
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    1. Zhai, Lu-Sheng & Liu, Ruo-Yu, 2019. "Local detrended cross-correlation analysis for non-stationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 222-233.

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