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Bootstrapping a weighted linear estimator of the ARCH parameters

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Bootstrapping a weighted linear estimator of the ARCH parameters. / Bose, Arup; Mukherjee, Kanchan.
In: Journal of Time Series Analysis, Vol. 30, No. 3, 05.2009, p. 315-331.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Bose A, Mukherjee K. Bootstrapping a weighted linear estimator of the ARCH parameters. Journal of Time Series Analysis. 2009 May;30(3):315-331. doi: 10.1111/j.1467-9892.2009.00613.x

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Bose, Arup ; Mukherjee, Kanchan. / Bootstrapping a weighted linear estimator of the ARCH parameters. In: Journal of Time Series Analysis. 2009 ; Vol. 30, No. 3. pp. 315-331.

Bibtex

@article{8d4060e3019447aead3d73eb05a31412,
title = "Bootstrapping a weighted linear estimator of the ARCH parameters",
abstract = "A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal.",
keywords = "ARCH model, QMLE , bootstrapping",
author = "Arup Bose and Kanchan Mukherjee",
year = "2009",
month = may,
doi = "10.1111/j.1467-9892.2009.00613.x",
language = "English",
volume = "30",
pages = "315--331",
journal = "Journal of Time Series Analysis",
issn = "0143-9782",
publisher = "Wiley-Blackwell",
number = "3",

}

RIS

TY - JOUR

T1 - Bootstrapping a weighted linear estimator of the ARCH parameters

AU - Bose, Arup

AU - Mukherjee, Kanchan

PY - 2009/5

Y1 - 2009/5

N2 - A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal.

AB - A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal.

KW - ARCH model

KW - QMLE

KW - bootstrapping

U2 - 10.1111/j.1467-9892.2009.00613.x

DO - 10.1111/j.1467-9892.2009.00613.x

M3 - Journal article

VL - 30

SP - 315

EP - 331

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 3

ER -