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The rescaled variance statistic and the determination of the Hurst exponent

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  • Cajueiro, Daniel O.
  • Tabak, Benjamin M.

Abstract

A major issue in statistical physics literature is the study of the long range dependence phenomenon usually presented in natural, social and financial processes. In particular, a big part of this literature relies on the determination of a parameter known as the Hurst exponent. Although many methods have been proposed to deal with this task, none of them are suitable for any time series and sometimes when applied to the same time series present conflicting results. In this context, this paper presents a new method based on the rescaled variance statistic which can be used efficiently to this end.

Suggested Citation

  • Cajueiro, Daniel O. & Tabak, Benjamin M., 2005. "The rescaled variance statistic and the determination of the Hurst exponent," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 172-179.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:3:p:172-179
    DOI: 10.1016/j.matcom.2005.06.005
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    Citations

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    Cited by:

    1. He, Ling-Yun & Qian, Wen-Bin, 2012. "A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3770-3782.
    2. Li, Wen & Yu, Cindy & Carriquiry, Alicia & Kliemann, Wolfgang, 2011. "The asymptotic behavior of the R/S statistic for fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 83-91, January.
    3. Rodríguez-Aguilar, Román & Cruz-Aké, Salvador & Venegas-Martínez, Francisco, 2014. "A Measure of Early Warning of Exchange-Rate Crises Based on the Hurst Coefficient and the Αlpha-Stable Parameter," MPRA Paper 59046, University Library of Munich, Germany.
    4. Qingfu Liu & Qian Luo & Yiuman Tse & Yuchi Xie, 2020. "The market quality of commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(11), pages 1751-1766, November.
    5. Cajueiro, Daniel O. & Tabak, Benjamin M., 2008. "Testing for long-range dependence in world stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 918-927.
    6. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Time-varying long-range dependence in US interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 360-367.
    7. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    8. Cajueiro, Daniel O. & Tabak, Benjamin M., 2010. "Fluctuation dynamics in US interest rates and the role of monetary policy," Finance Research Letters, Elsevier, vol. 7(3), pages 163-169, September.
    9. Ding, Liang & Luo, Yi & Lin, Yan & Huang, Yirong, 2021. "Revisiting the relations between Hurst exponent and fractional differencing parameter for long memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    10. Guo, Wenjing & Li, Sijie & Xing, Mengyue & Lin, Shengyao, 2023. "Evaluation of the operational quality of China's grain futures market based on the comprehensive information weighting method," International Review of Economics & Finance, Elsevier, vol. 86(C), pages 467-482.
    11. Cajueiro, Daniel O. & Tabak, Benjamin M., 2007. "Is the expression H=1/(3-q) valid for real financial data?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 593-602.

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