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Performance of a high-dimensional R/S method for Hurst exponent estimation

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  • Alvarez-Ramirez, Jose
  • Echeverria, Juan C.
  • Rodriguez, Eduardo

Abstract

An extension of the R/S method to estimate the Hurst exponent of high-dimensional fractals is proposed. The method’s performance was adequate when tested with synthetic surfaces having different preset Hurst exponent values and different array sizes. The two-dimensional R/S analysis is used to analyze three images from nature and experimental data, revealing interesting scaling behavior with physical meaning.

Suggested Citation

  • Alvarez-Ramirez, Jose & Echeverria, Juan C. & Rodriguez, Eduardo, 2008. "Performance of a high-dimensional R/S method for Hurst exponent estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6452-6462.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:26:p:6452-6462
    DOI: 10.1016/j.physa.2008.08.014
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    References listed on IDEAS

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    1. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    2. Caccia, David C. & Percival, Donald & Cannon, Michael J. & Raymond, Gary & Bassingthwaighte, James B., 1997. "Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 609-632.
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    Cited by:

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    5. Xi, Caiping & Zhang, Shunning & Xiong, Gang & Zhao, Huichang, 2016. "A comparative study of two-dimensional multifractal detrended fluctuation analysis and two-dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 34-50.
    6. Ji, Li-Jun & Zhou, Wei-Xing & Liu, Hai-Feng & Gong, Xin & Wang, Fu-Chen & Yu, Zun-Hong, 2009. "R/S method for unevenly sampled time series: Application to detecting long-term temporal dependence of droplets transiting through a fixed spatial point in gas–liquid two-phase turbulent jets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3345-3354.
    7. Pakrashi, Vikram & Kelly, Joe & Harkin, Julie & Farrell, Aidan, 2013. "Hurst exponent footprints from activities on a large structural system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1803-1817.
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    9. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    10. Mulligan, Robert F., 2014. "Multifractality of sectoral price indices: Hurst signature analysis of Cantillon effects in disequilibrium factor markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 252-264.

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