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Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search

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  • Li, Ming
  • Zhang, Peidong
  • Leng, Jianxing

Abstract

This article presents an improved autocorrelation correlation function (ACF) regression method of estimating the Hurst parameter of a time series with long-range dependence (LRD) by using golden section search (GSS). We shall show that the present method is substantially efficient than the conventional ACF regression method of H estimation. Our research uses fractional Gaussian noise as a data case but the method introduced is applicable to time series with LRD in general.

Suggested Citation

  • Li, Ming & Zhang, Peidong & Leng, Jianxing, 2016. "Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 189-199.
    • Handle: RePEc:eee:phsmap:v:445:y:2016:i:c:p:189-199
    DOI: 10.1016/j.physa.2015.10.071
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    1. Li, Muyi & Huang, Yongxiang, 2014. "Hilbert–Huang Transform based multifractal analysis of China stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 222-229.
    2. Li, Ming & Lim, S.C., 2008. "Modeling network traffic using generalized Cauchy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2584-2594.
    3. Leonenko, N.N. & Sakhno, L.M., 2006. "On the Whittle estimators for some classes of continuous-parameter random processes and fields," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 781-795, April.
    4. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    5. Ayache, Antoine & Roueff, François & Xiao, Yimin, 2009. "Linear fractional stable sheets: Wavelet expansion and sample path properties," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1168-1197, April.
    6. B. Podobnik & D. F. Fu & H. E. Stanley & P. Ch. Ivanov, 2007. "Power-law autocorrelated stochastic processes with long-range cross-correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(1), pages 47-52, March.
    7. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    8. Yin, Xin-An & Yang, Xiao-Hua & Yang, Zhi-Feng, 2009. "Using the R/S method to determine the periodicity of time series," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 731-745.
    9. Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Peng, C.-K. & Simons, M., 1993. "Long-range power-law correlations in condensed matter physics and biophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 4-24.
    10. Shang, Pengjian & Lu, Yongbo & Kama, Santi, 2006. "The application of Hölder exponent to traffic congestion warning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 769-776.
    11. Ian Affleck, 2010. "Golden ratio seen in a magnet," Nature, Nature, vol. 464(7287), pages 362-363, March.
    12. Céline Lévy‐Leduc & Hélène Boistard & Eric Moulines & Murad S. Taqqu & Valderio A. Reisen, 2011. "Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 135-156, March.
    13. Mielniczuk, J. & Wojdyllo, P., 2007. "Estimation of Hurst exponent revisited," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4510-4525, May.
    14. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    15. I. Lubashevsky, 2011. "Truncated Lévy flights and generalized Cauchy processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 82(2), pages 189-195, July.
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    Cited by:

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