Parameter estimation in nonlinear AR-GARCH models
This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors.� We consider a functional coefficient 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.� 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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