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Mixed-correlated ARFIMA processes for power-law cross-correlations

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  • Kristoufek, Ladislav

Abstract

We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when Hxy=12(Hx+Hy), MC-ARFIMA also allows for processes with Hxy<12(Hx+Hy) but also for long-range correlated processes which are either short-range cross-correlated or simply correlated. The major contribution of MC-ARFIMA lies in the fact that the processes have well-defined asymptotic properties for Hx, Hy and Hxy, which are derived in the paper, so that the processes can be used in simulation studies comparing various estimators of the bivariate Hurst exponent Hxy. Moreover, the framework allows for modeling of processes which are found to have Hxy<12(Hx+Hy).

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  • Kristoufek, Ladislav, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6484-6493.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:24:p:6484-6493
    DOI: 10.1016/j.physa.2013.08.041
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    7. 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).
    8. Kristoufek, Ladislav & Lunackova, Petra, 2015. "Rockets and feathers meet Joseph: Reinvestigating the oil–gasoline asymmetry on the international markets," Energy Economics, Elsevier, vol. 49(C), pages 1-8.
    9. Cao, Guangxi & Shi, Yingying, 2017. "Simulation analysis of multifractal detrended methods based on the ARFIMA process," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 235-243.
    10. Wang, Fang & Wang, Lin & Chen, Yuming, 2018. "Quantifying the range of cross-correlated fluctuations using a q–L dependent AHXA coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 454-464.
    11. Kristoufek, Ladislav, 2015. "Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 124-127.
    12. Kristoufek, Ladislav, 2014. "Measuring correlations between non-stationary series with DCCA coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 291-298.
    13. 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.
    14. Teng, Yue & Shang, Pengjian, 2017. "Transfer entropy coefficient: Quantifying level of information flow between financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 60-70.
    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.
    16. Ladislav Kristoufek, 2014. "Spectrum-based estimators of the bivariate Hurst exponent," Papers 1408.6637, arXiv.org, revised Nov 2014.
    17. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
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