We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The...

We study the strong consistency and asymptotic normality of the maximum likelihood estimator for a class of time series models driven by the score function of the predictive likelihood. This class of nonlinear dynamic models includes both new and existing observation driven time series models....

We investigate the information theoretic optimality properties of the score function of the predictive likelihood as a device to update parameters in observation driven time-varying parameter models. The results provide a new theoretical justification for the class of generalized autoregressive...

The strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the...

We introduce a new estimation framework which extends the Generalized Method of Moments (GMM) to settings where a subset of the parameters vary over time with unknown dynamics. To filter out the dynamic path of the time-varying parameter, we approximate the dynamics by an autoregressive process...