Godambe (1960,1985) and Hansen (1982) proposed the method of estimating function which makes a bridge between least squares estimator and maximum likelihood estimator. In this paper we apply the estimating function approach to CHARN models which include many well-known nonlinear time series models as special cases. Since the estimation function does not always yield the asymptotically efficient estimator, we give the optimal estimating function which entails the asymptotic efficient estimator. Numerical studies are provided, and they show some interesting features of the asymptotics.
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