Abstract
We give an evaluation of limit variance in the central limit theorem for waveletbased estimator of the Hurst index of fractional Brownian motion (FBM). is the variance of a certain linear sum (with respect to scale j ) of random variables. As a result, contribution to variance of the linear form turns out to be mostly its diagonal part components, which can be considered as a form of frequency localization (FL) property of wavelet coefficients of FBM. This FL property, together with specifiability of small J behavior of , is applied to determine the optimal upper bound of scale j used in the estimation.
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