Functional-Coefficient Regression Models for Nonlinear Time Series
- Author(s): Cai, Zongwu;
- Fan, Jianqing;
- Yao, Qiwei
- et al.
We apply the local linear regression technique for estimation of functional-cefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functional-coefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better post-sample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and is of appreciable 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 alpha-mixing condition. Both simulated and real data examples are used for illustration.