Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

Jean Marc Bardet; Ciprian Tudor

doi:10.1016/j.jmva.2014.06.012

Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

Jean Marc Bardet
, Ciprian Tudor

Université Panthéon-Sorbonne (Paris 1)
CNRS UMR 8524
Academy of Economical Studies
Academy of Economical Studies

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

12 Citations (Scopus)

Abstract

The purpose of this paper is the estimation of the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Journal of Multivariate Analysis
Volume	131
DOIs	https://doi.org/10.1016/j.jmva.2014.06.012
Publication status	Published - 1 Jan 2014
Externally published	Yes

Keywords

Long-memory process
Multiple Wiener-ItÔ integrals
Non-central limit theorem
Rosenblatt process
Whittle estimator

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10.1016/j.jmva.2014.06.012

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title = "Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process",

abstract = "The purpose of this paper is the estimation of the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.",

keywords = "Long-memory process, Multiple Wiener-It{\^O} integrals, Non-central limit theorem, Rosenblatt process, Whittle estimator",

author = "Bardet, \{Jean Marc\} and Ciprian Tudor",

year = "2014",

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doi = "10.1016/j.jmva.2014.06.012",

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AU - Bardet, Jean Marc

AU - Tudor, Ciprian

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N2 - The purpose of this paper is the estimation of the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

AB - The purpose of this paper is the estimation of the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

KW - Long-memory process

KW - Multiple Wiener-ItÔ integrals

KW - Non-central limit theorem

KW - Rosenblatt process

KW - Whittle estimator

U2 - 10.1016/j.jmva.2014.06.012

DO - 10.1016/j.jmva.2014.06.012

M3 - Article

AN - SCOPUS:84903850884

SN - 0047-259X

VL - 131

SP - 1

EP - 16

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

ER -

Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

Abstract

Keywords

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