The Asymptotics of ARMA Estimators in 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