Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

被引：23

作者：

Bardet, Jean-Marc ^{[1
]}

Surgailis, Donatas ^{[2
]}

机构：

[1] Univ Paris 01, SAMM, F-75634 Paris, France

[2] Inst Math & Informat, Vilnius, Lithuania

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2013年 / 123卷 / 03期

关键词：

Nonparametric estimators; Hurst function; Tangent process; Multifractional Brownian motion; Gaussian process; Central limit theorem; QUADRATIC VARIATIONS; BROWNIAN-MOTION; LIMIT-THEOREMS; IDENTIFICATION;

D O I：

10.1016/j.spa.2012.11.009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：1004 / 1045

页数：42

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