Jianhua Z. Huang

Abstract. We propose a global smoothing method based on polynomial splines for the estimation of functional coefficient regression models for non‐linear 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 forecasts and density forecasts. The methodology is illustrated by simulations and two real data examples.

Summary: We propose a lag selection method for non-linear additive autoregressive models that is based on spline estimation and the Bayes information criterion. The additive structure of the autoregression function is used to overcome the ‘curse of dimensionality’, whereas the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the method proposed. A comprehensive Monte Carlo study demonstrates good performance of the method proposed and a substantial computational advantage over existing local-polynomial-based methods. Consistency of the lag selection method based on the Bayes information criterion is established under the assumption that the observations are from a stochastic process that is strictly stationary and strongly mixing, which provides the first theoretical result of this kind for spline smoothing of weakly dependent data.