Nonparametric estimation of additive nonlinear ARX time series: Local linear fitting and projections

We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a l ocal polynomial fitting scheme coupled with projections. We establish the w eak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given.