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PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS

Published online by Cambridge University Press:  31 May 2011

Mika Meitz  and
Pentti Saikkonen
Mika Meitz*
Affiliation:
Koç University
Pentti Saikkonen*
Affiliation:
University of Helsinki
*
*Address correspondence to: Mika Meitz, Department of Economics, Koç University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey; e-mail: mmeitz@ku.edu.tr; or to: Pentti Saikkonen, Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, FIN–00014 University of Helsinki, Finland; e-mail: pentti.saikkonen@helsinki.fi.
*Address correspondence to: Mika Meitz, Department of Economics, Koç University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey; e-mail: mmeitz@ku.edu.tr; or to: Pentti Saikkonen, Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, FIN–00014 University of Helsinki, Finland; e-mail: pentti.saikkonen@helsinki.fi.
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Abstract

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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ARTICLES
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Econometric Theory , Volume 27 , Issue 6 , December 2011 , pp. 1236 - 1278
Copyright
Copyright © Cambridge University Press 2011

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