Nonparametric Transfer Function Models: A Polynomial Spline Approach

Nonparametric transfer models have been developed to model nonlinear relationships between input and output time series. In this paper we consider a polynomial spline-based estimation method of such models. The transfer function is assumed to be smooth but the functional form unknown. The noise is assumed to follow a parametric ARIMA model. The transfer function is modeled using polynomial splines and estimated jointly with the ARIMA parameters. Compared with existing local polynomial-based approaches, the use of regression splines not only reduces the computational complexity, but also allows the noise to be nonstationary. The estimation procedures are introduced and the asymptotic properties of the estimators are discussed. The finite-sample properties of the estimators are studied through simulations and one real example.