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Bootstrapping a weighted linear estimator of the ARCH parameters

Bose, Arup and Mukherjee, Kanchan (2009) Bootstrapping a weighted linear estimator of the ARCH parameters. Journal of Time Series Analysis, 30 (3). pp. 315-331. ISSN 1467-9892

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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.

Item Type: Article
Journal or Publication Title: Journal of Time Series Analysis
Uncontrolled Keywords: ARCH model ; QMLE ; bootstrapping
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 54451
Deposited By: ep_importer_pure
Deposited On: 22 May 2012 15:18
Refereed?: Yes
Published?: Published
Last Modified: 24 Jan 2014 05:27
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/54451

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