Cai, Zongwu, Fan, Jianqing and Yao, Qiwei 
ORCID: 0000-0003-2065-8486
(2000)
Functional-coefficient regression models for nonlinear time series.
Journal of the American Statistical Association, 95 (451).
pp. 941-956.
ISSN 0162-1459
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.
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