The Asymptotic Behavior of ARMA Estimators in Multi-Dimensional Spline-Backfitted Transfer Function Models

In this paper a new method to model the noise term in multidimensional nonparametric transfer functions is proposed. The transfer function is assumed to be additive and estimated using the spline-backfitted kernel estimator. In spline-backfitted kernel models, under a general mixing condition on the noise, an additive component of the transfer function can be estimated asymptotically as if the other components are known by "oracle". In this paper, the noise is allowed to follow an Autoregressive-Moving Average (ARMA) process. With this new assumption, the "oracle" property of the spline-backfit estimators remain, additionally, the ARMA parameters can be estimated asymptotically as if the transfer function is known. This method allows the noise to be modeled explicitly as a parsimonious ARMA process, which improves the estimation efficiency and forecasting accuracy.