Bootstrapping a Weighted Linear Estimator of the Arch Parameters

17 Pages Posted: 27 Apr 2009

See all articles by Arup Bose

Arup Bose

Indian Statistical Institute, Kolkata - Statistics and Mathematics Unit

Kanchan Mukherjee

Indian Institute of Management (IIMB), Bangalore

Date Written: 0000

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.

Suggested Citation

Bose, Arup and Mukherjee, Kanchan, Bootstrapping a Weighted Linear Estimator of the Arch Parameters (0000). Journal of Time Series Analysis, Vol. 30, Issue 3, pp. 315-331, May 2009, Available at SSRN: https://ssrn.com/abstract=1392489 or http://dx.doi.org/10.1111/j.1467-9892.2009.00613.x

Arup Bose (Contact Author)

Indian Statistical Institute, Kolkata - Statistics and Mathematics Unit ( email )

India

Kanchan Mukherjee

Indian Institute of Management (IIMB), Bangalore ( email )

Bannerghatta Road
Bangalore, Karnataka 560076
India

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