Econometric Theory

Notes and Problems

QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF SEMI-STRONG GARCH MODELS

Juan Carlos Escancianoa1 c1

a1 Indiana University

Abstract

This note proves the consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (GARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994, Econometric Theory 10, 29–52) for the local QMLE in semistrong GARCH(1,1) models. In particular, no restrictions on the conditional mean are imposed. Our proofs closely follow those in Francq and Zakoïan (2004, Bernoulli 10, 605–637) for independent and identically distributed innovations.

Correspondence

c1 Address correspondence to Juan Carlos Escanciano, Indiana University, Department of Economics, 100 S. Woodlawn, Wylie Hall, Bloomington, IN 47405-7104, U.S.A.; e-mail: jescanci@indiana.edu.

Footnotes

The note has benefited from the comments of three referees, the co-editor, Paolo Paruolo, and Emma Iglesias. This research was funded by the Spanish Plan Nacional de I+D+I, reference number SEJ2007-62908.

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