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Estimating long range dependence: finite sample properties and confidence intervals


  • Rafal Weron


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.

Suggested Citation

  • Rafal Weron, 2001. "Estimating long range dependence: finite sample properties and confidence intervals," HSC Research Reports HSC/01/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0103

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    References listed on IDEAS

    1. Baillie, Richard T. & King, Maxwell L., 1996. "Editors' introduction: Fractional differencing and long memory processes," Journal of Econometrics, Elsevier, vol. 73(1), pages 1-3, July.
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    More about this item


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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions


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