Functional-Coefficient Regression Models for Nonlinear Time Series

Abstract

The local linear regression technique is applied to estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models and functional-coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. Also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and of sufficient flexibility to analyze complex and multivariate nonlinear structures without suffering from the “curse of dimensionality.” The asymptotic properties of the proposed estimators are investigated under the α-mixing condition. Both simulated and real data examples are used for illustration.

Key Words:

• α-mixing
• Asymptotic normality
• Bootstrap
• Forecasting
• Goodness-of-fit test
• Local linear regression
• Nonlinear time series
• Varying-coefficient models