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Estimating long range dependence: finite sample properties and confidence intervals

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  • Rafal Weron

Abstract

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/S statistics and are very close to asymptotic values for the periodogram regression method.

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File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_01_03.pdf
File Function: Final draft, 2001
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File URL: http://dx.doi.org/10.1016/S0378-4371(02)00961-5
File Function: Final printed version, 2002
Download Restriction: Yes

Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/01/03.

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Length: 15 pages
Date of creation: 2001
Date of revision:
Publication status: Published in Physica A 312 (2002) 285-299.
Handle: RePEc:wuu:wpaper:hsc0103

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Keywords: Long-range dependence; Hurst exponent; R/S analysis; Detrended Fluctuation Analysis; Periodogram regression; Confidence interval;

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Cited by:
  1. Jozef Barunik & Ladislav Kristoufek, 2012. "On Hurst exponent estimation under heavy-tailed distributions," Papers 1201.4786, arXiv.org.
  2. Ladislav Kristoufek & Miloslav Vosvrda, 2012. "Measuring capital market efficiency: Global and local correlations structure," Papers 1208.1298, arXiv.org.
  3. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
  4. Rafal Weron, 2001. "Measuring long-range dependence in electricity prices," Papers cond-mat/0103621, arXiv.org.
  5. Kristoufek, Ladislav, 2012. "How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4252-4260.
  6. Ladislav Krištoufek, 2010. "Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009," Politická ekonomie, University of Economics, Prague, vol. 2010(4), pages 471-487.
  7. Zhi-Qiang Jiang & Wen-Jie Xie & Wei-Xing Zhou, 2012. "Testing the weak-form efficiency of the WTI crude oil futures market," Papers 1211.4686, arXiv.org.
  8. Fernández, Isabel & Pacheco, José M. & Quintana, María P., 2010. "Pinkness of the North Atlantic Oscillation signal revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5801-5807.
  9. Kristoufek, Ladislav, 2009. "Distinguishing between short and long range dependence: Finite sample properties of rescaled range and modified rescaled range," MPRA Paper 16424, University Library of Munich, Germany.
  10. Pirino, Davide, 2009. "Jump detection and long range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1150-1156.
  11. Kristoufek, Ladislav, 2009. "Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009
    [Long-term memory and its evolution in returns of PX between 1999 and 2009]
    ," MPRA Paper 16435, University Library of Munich, Germany.
  12. Cajueiro, Daniel O. & Gogas, Periklis & Tabak, Benjamin M., 2009. "Does financial market liberalization increase the degree of market efficiency? The case of the Athens stock exchange," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 50-57, March.
  13. Jia, Zhanliang & Cui, Meilan & Li, Handong, 2012. "Research on the relationship between the multifractality and long memory of realized volatility in the SSECI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 740-749.
  14. Turvey, Calum G., 2007. "A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 155-165.
  15. Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
  16. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.
  17. Lopes, S.R.C. & Nunes, M.A., 2006. "Long memory analysis in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 569-588.
  18. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.

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