Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths

被引：1
作者：
Jean-François Coeurjolly
机构：
[1] University Joseph Fourier,IMAG
来源：
Statistical Inference for Stochastic Processes | 2001年 / 4卷 / 2期
关键词：
fractional Brownian motion; fractional Gaussian noise; discrete variations; consistency; self-similarity;
D O I：
10.1023/A:1017507306245
中图分类号：
学科分类号：
摘要：
This paper develops a class of consistent estimators of the parameters of a fractional Brownian motion based on the asymptotic behavior of the k-th absolute moment of discrete variations of its sampled paths over a discrete grid of the interval [0,1]. We derive explicit convergence rates for these types of estimators, valid through the whole range 0 < H < 1 of the self-similarity parameter. We also establish the asymptotic normality of our estimators. The effectiveness of our procedure is investigated in a simulation study.
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页码：199 / 227
页数：28
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