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

Wen Li, Cindy Yu, Alicia Carriquiry and Wolfgang Kliemann

Statistics & Probability Letters, 2011, vol. 81, issue 1, 83-91

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.

Keywords: Fractional; Brownian; motion; Hurst; exponent; Self-similarity; index (search for similar items in EconPapers)
Date: 2011
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