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Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator

Published online by Cambridge University Press:  11 February 2009

Sang-Won Lee  and
Bruce E. Hansen
Sang-Won Lee
Affiliation:
Indiana University
Bruce E. Hansen
Affiliation:
University of Rochester
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Abstract

This paper investigates the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. The rescaled variable (the ratio of the disturbance to the conditional standard deviation) is not required to be Gaussian nor independent over time, in contrast to the current literature. The GARCH process may be integrated (α + β = 1), or even mildly explosive (α + β > 1). A bounded conditional fourth moment of the rescaled variable is sufficient for the results. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.

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Type
Articles
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Econometric Theory , Volume 10 , Issue 1 , March 1994 , pp. 29 - 52
Copyright
Copyright © Cambridge University Press 1994

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