Nonlinear autoregressive exogenous time series: structural identification via projection estimates

We consider additive nonlinear autoregressive exogenous (ARX) time series and propose projections as means of identifying and estimating its endogenous and exogenous components. The estimates are nonparametric in nature and involve averaging of kernel type estimates. Such estimates have been treated informally in a univariate time series situation. We extend the scope to nonlinear ARX models and present a rigorous theory, including the establishment of consistency and asymptotic normality for the projection estimates.