Functional Coefficient Regression Models for Nonlinear Time series: 
A Polynomial Spline Approach

Jianhua Z. Huang and Haipeng Shen
July 2002

We propose a global smoothing method based on polynomial splines
for the estimation of functional coefficient regression models for nonlinear
time series. Consistency and rate of convergence results are given to support
the proposed estimation method. Methods for automatic selections
of the threshold variable and significant variables (or lags) are developed.
The estimated model is used to produce multi-step-ahead forecasts, including
interval forecasts and density forecasts. The methodology is illustrated
by simulations and an application to the US GNP time series.