Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Jean Marc Bardet; Donatas Surgailis

doi:10.1016/j.spa.2012.11.009

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1004-1045
Number of pages	42
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	3
DOIs	https://doi.org/10.1016/j.spa.2012.11.009
Publication status	Published - 2 Jan 2013
Externally published	Yes

Keywords

Central limit theorem
Gaussian process
Hurst function
Multifractional Brownian motion
Nonparametric estimators
Tangent process

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10.1016/j.spa.2012.11.009

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title = "Nonparametric estimation of the local Hurst function of multifractional Gaussian processes",

abstract = "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.",

keywords = "Central limit theorem, Gaussian process, Hurst function, Multifractional Brownian motion, Nonparametric estimators, Tangent process",

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AU - Bardet, Jean Marc

AU - Surgailis, Donatas

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N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Gaussian process

KW - Hurst function

KW - Multifractional Brownian motion

KW - Nonparametric estimators

KW - Tangent process

U2 - 10.1016/j.spa.2012.11.009

DO - 10.1016/j.spa.2012.11.009

M3 - Article

AN - SCOPUS:84871642579

SN - 0304-4149

VL - 123

SP - 1004

EP - 1045

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 3

ER -

Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Abstract

Keywords

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