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The asymptotic behavior of the R/S statistic for fractional Brownian motion
Authors:Wen Li  Cindy Yu  Wolfgang Kliemann
Institution:
  • a Department of Statistics, Iowa State University, Ames, IA 50011, USA
  • b Department of Mathematics, Iowa State University, Ames, IA 50011, USA
  • 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
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