On the prediction for some nonlinear time series models using estimating functions

Godambe's (1960, 1985) theorems on optimal estimating equations are applied to some non-linear, non-Gaussian time series prediction problems. (Examples are considered from the usual class of time series models.) Recently many researchers in applied time series analysis attracted the information and valid analysis provided by the estimating equation approach. Therefore this article places an interest of estimating equation (EE) prediction theory and building a link between it and the well-known minimum mean square error (MMSE) prediction methodology. Superiority of this EE prediction method over the MMSE is investigated. In particular a random coefficient autoregressive model is discussed in some detail using these EE and MMSE theories.