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FIRST-ORDER ASYMPTOTIC THEORY FOR PARAMETRIC MISSPECIFICATION TESTS OF GARCH MODELS

Published online by Cambridge University Press:  01 April 2009

Andreea G. Halunga  and
Chris D. Orme
Andreea G. Halunga*
Affiliation:
University of Exeter
Chris D. Orme
Affiliation:
University of Manchester
*
*Address correspondence to Andreea G. Halunga, Department of Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter EX4 4PU, United Kingdom; e-mail: a.g.halunga@exeter.ac.uk.
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Abstract

This paper develops a framework for the construction and analysis of parametric misspecification tests for generalized autoregressive conditional heteroskedastic (GARCH) models, based on first-order asymptotic theory. The principal finding is that estimation effects from the correct specification of the conditional mean (regression) function can be asymptotically nonnegligible. This implies that certain procedures, such as the asymmetry tests of Engle and Ng (1993, Journal of Finance 48, 1749–1777) and the nonlinearity test of Lundbergh and Teräsvirta (2002, Journal of Econometrics 110, 417–435), are asymptotically invalid. A second contribution is the proposed use of alternative tests for asymmetry and/or nonlinearity that, it is conjectured, should enjoy improved power properties. A Monte Carlo study supports the principal theoretical findings and also suggests that the new tests have fairly good size and very good power properties when compared with the Engle and Ng (1993) and Lundbergh and Teräsvirta (2002) procedures.

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Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 2 , April 2009 , pp. 364 - 410
Copyright
Copyright © Cambridge University Press 2009

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