Functional coefficient regression models for nonlinear time series: A polynomial spline approach

ABSTRACT. We propose a global smoothing method based on polynomial splines for the es-timation 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 selection of the threshold variable and significant variables (or lags) are discussed. The estimated model is used to produce multi-step-ahead forecasts, including interval fore-casts and density forecasts. The methodology is illustrated by simulations and two real data examples. Key words: forecasting, functional autoregressive model, nonparametric regression, threshold autoregressive model, varying coefficient model. Running Heading: Functional coefficient models with splines.