Wavelet linear density estimation for a GARCH model under various dependence structures

Christophe Chesneau; Hassan Doosti

Wavelet linear density estimation for a GARCH model under various dependence structures

Christophe Chesneau^*, Hassan Doosti

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

We consider n observations from the GARCH-type model: S = σ²Z, where σ² and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ² under four different dependence structures: the strong mixing case, the β-mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are explored. In each case, we prove that it attains a fast rate of convergence.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Journal of the Iranian Statistical Society
Volume	11
Issue number	1
Publication status	Published - 2012
Externally published	Yes

Keywords

Dependent sequence
GARCH models
Linear estimator
Rate of convergence
Wavelets

Cite this

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abstract = "We consider n observations from the GARCH-type model: S = σ2Z, where σ2 and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ2 under four different dependence structures: the strong mixing case, the β-mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are explored. In each case, we prove that it attains a fast rate of convergence.",

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AU - Chesneau, Christophe

AU - Doosti, Hassan

PY - 2012

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N2 - We consider n observations from the GARCH-type model: S = σ2Z, where σ2 and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ2 under four different dependence structures: the strong mixing case, the β-mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are explored. In each case, we prove that it attains a fast rate of convergence.

AB - We consider n observations from the GARCH-type model: S = σ2Z, where σ2 and Z are independent random variables. We develop a new wavelet linear estimator of the unknown density of σ2 under four different dependence structures: the strong mixing case, the β-mixing case, the pairwise positive quadrant case and the ρ-mixing case. Its asymptotic mean integrated squared error properties are explored. In each case, we prove that it attains a fast rate of convergence.

KW - Dependent sequence

KW - GARCH models

KW - Linear estimator

KW - Rate of convergence

KW - Wavelets

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M3 - Article

AN - SCOPUS:84871478237

SN - 1726-4057

VL - 11

SP - 1

EP - 21

JO - Journal of the Iranian Statistical Society

JF - Journal of the Iranian Statistical Society

IS - 1

ER -

Wavelet linear density estimation for a GARCH model under various dependence structures

Abstract

Keywords

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