Functional-Coefficient Autoregressive Models

Abstract

In this article we propose a new class of models for nonlinear time series analysis, investigate properties of the proposed model, and suggest a modeling procedure for building such a model. The proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics. A consistency result is given to support the procedure. For illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially improve postsample multi-step ahead forecasts over other models.

KEY WORDS:

• Arranged local regression
• Consistency
• Forecasting
• Geometrical ergodicity
• Nonlinear time series
• Threshold autoregressive model