Fisher Information for Fractional Brownian Motion Under High-Frequency Discrete Sampling |
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Authors: | Reiichiro Kawai |
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Affiliation: | 1. School of Mathematics and Statistics , University of Sydney , Sydney , Australia reiichiro.kawai@maths.usyd.edu.au |
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Abstract: | We investigate the issue of the validation of the local asymptotic normality property of three characterizing parameters of the fractional Brownian motion under high-frequency discrete sampling. We prove that the local asymptotic normality property holds true for the likelihood only when at least one of the volatility parameter and the Hurst exponent is known. We provide optimal rates of convergence of the three parameters and Fisher information matrix in closed form. |
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Keywords: | Fractional Brownian motion High-frequency sampling Local asymptotic normality property Log-likelihood ratios Long-range dependence Parametric estimation |
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