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A CLOSED-FORM ESTIMATOR FOR THE GARCH(1,1) MODEL

Published online by Cambridge University Press:  09 February 2006

Dennis Kristensen  and
Oliver Linton
Dennis Kristensen
Affiliation:
University of Wisconsin-Madison
Oliver Linton
Affiliation:
London School of Economics
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Abstract

We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and -asymptotic normality when the eighth moment exists. We demonstrate that a finite number of Newton–Raphson iterations using our estimator as starting point will yield asymptotically the same distribution as the QMLE when the fourth moment exists. A simulation study confirms our theoretical results.The first author's research was supported by the Shoemaker Foundation. The second author's research was supported by the Economic and Social Science Research Council of the United Kingdom.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 22 , Issue 2 , April 2006 , pp. 323 - 337
Copyright
© 2006 Cambridge University Press

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