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Power-law cross-correlations estimation under heavy tails

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  • Ladislav Kristoufek

Abstract

We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle estimator -- under heavy-tailed distributions. The selection of estimators allows to separate these into the time and frequency domain estimators. By varying the characteristic exponent of the $\alpha$-stable distributions which controls the tails behavior, we report several interesting findings. First, the frequency domain estimators are practically unaffected by heavy tails bias-wise. Second, the time domain estimators are upward biased for heavy tails but they have lower estimator variance than the other group for short series. Third, specific estimators are more appropriate depending on distributional properties and length of the analyzed series. In addition, we provide a discussion of implications of these results for empirical applications as well as theoretical explanations.

Suggested Citation

  • Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.
  • Handle: RePEc:arx:papers:1602.05385
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    References listed on IDEAS

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    Cited by:

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    5. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Casado Belmonte, M.P. & Trinidad Segovia, J.E., 2020. "A note on power-law cross-correlated processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Xi, Caiping & Zhang, Shuning & Xiong, Gang & Zhao, Huichang & Yang, Yonghong, 2017. "The application of the multifractal cross-correlation analysis methods in radar target detection within sea clutter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 839-854.
    7. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 658-670.

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