Additive nonlinear ARX time series and projection estimates

We propose projections as means of identifying and estimating the com ponents (endogenous and exogenous) of an additive nonlinear ARX m odel. The estimates are nonparametric in nature and involve ave ra ging of kernal-type estimates. Such estimates have recently been t reated informally in a univariate time series situation. Here we ext end the scope to nonlinear ARX models and present a rigorous theo ry, including the derivation of asymptotic normality for the pro j ection estimates under a precise set of regularity conditions.