The asymptotic behavior of the R/S statistic for fractional Brownian motion |
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Authors: | Wen Li Cindy Yu Wolfgang Kliemann |
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Institution: | a Department of Statistics, Iowa State University, Ames, IA 50011, USAb Department of Mathematics, Iowa State University, Ames, IA 50011, USA |
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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. |
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Keywords: | Fractional Brownian motion Hurst exponent Self-similarity index |
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