Spline-Backfitted Additive Nonparametric Transfer Function Models

In this paper we consider additive modeling of multi-dimensional nonlinear transfer functions with ARMA type of noise. Polynomial splines are used to obtain preliminary estimates of the additive transfer function components jointly with the ARMA parameters. These preliminary estimates are then used in backfitting to obtain final estimates of the transfer function components, using local polynomial regression. By showing that the errors caused by spline approximation in the preliminary estimation is negligible, it can be shown that an additive component can be estimated by local polynomial asymptotically as if the other components and the ARMA parameters are known. This spline-backfitted estimator is less computationally intensive than a full-blown local polynomial additive model, and its asymptotic properties are easier to derive than a full-blown polynomial spline additive model.