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The asymptotic behavior of the R/S statistic for fractional Brownian motion

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  • Li, Wen
  • Yu, Cindy
  • Carriquiry, Alicia
  • Kliemann, Wolfgang

Abstract

This paper provides a proof of the fact that asymptotically the R/S statistic and the self-similarity index of fractional Brownian motion agree in the expectation sense. In particular for fractional Gaussian noise time series, the R/S statistic is an estimator of the self-similarity index H. We also show that two other methods for estimating H yield consistent estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:83-91
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