Asymptotic expansion of an estimator for the Hurst coefficient

IF 0.7 Q3 STATISTICS & PROBABILITY

Statistical Inference for Stochastic Processes Pub Date : 2023-09-25 DOI:10.1007/s11203-023-09298-8

Yuliya Mishura, Hayate Yamagishi, Nakahiro Yoshida

引用次数: 0

Abstract

Abstract Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. We first derive the expansion formula of the principal term of the error of the estimator using a recently developed theory of asymptotic expansion of the distribution of Wiener functionals, and utilize the perturbation method on the obtained formula in order to calculate the expansion of the estimator. We also discuss some second-order modifications of the estimator. Numerical results show that the asymptotic expansion attains higher accuracy than the normal approximation.

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赫斯特系数估计量的渐近展开式

摘要给出了分数阶布朗运动赫斯特系数估计量的渐近展开式。我们首先利用最近发展的Wiener泛函分布渐近展开理论，推导了估计量误差主项的展开式，并利用摄动法对得到的公式进行了估计量展开式的计算。我们还讨论了估计量的一些二阶修正。数值结果表明，渐近展开法比正态逼近法具有更高的精度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Inference for Stochastic Processes STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

12.50%

发文量

期刊介绍： Statistical Inference for Stochastic Processes aims to publish high quality papers devoted to inference in either discrete or continuous time stochastic processes. This includes topics such as ARMA processes, GARCH processes and other time series models, as well as diffusion type processes, point processes, random fields and Markov processes. Papers related to spatial models and empirical processes are also within the scope of the journal. Special focus is placed on methodological advances and sound theoretical results, but submissions that expose potential applications of the developed theory to finance, insurance, economics, biology, physics and engineering are very much encouraged. Officially cited as: Stat Inference Stoch Process