On estimating the spectral exponent of fractional Brownian motion |
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Authors: | Jenn-Sen Leu Papamarcou A. |
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Affiliation: | Dept. of Electr. Eng., Maryland Univ., College Park, MD; |
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Abstract: | Three estimators of the exponent α in the power spectral density g(λ)=cg|λ|-α of fractional Brownian motion are evaluated. These are (i) the periodogram-based estimator αˆPG (ii) the maximum likelihood estimator αˆML; and (iii) the Allan (1966) variance-based estimator αˆAV. Large-sample properties of the mean-square error (MSE) and the associated sampling distribution are examined, αˆPG emphasis on the case α∈(1, 2). The MSE performance of αˆPG is judged to be inferior to that of both αˆML and αˆAV. The rate of decrease of MSE is the same for αˆML and αˆAV; the former estimator has smaller MSE, while the latter is less sensitive to departures from the power-law model and is considerably easier to compute |
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