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Functional-coefficient regression models for nonlinear time series. (English) Zbl 0996.62078
Summary: 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 crossvalidatory 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 $$\alpha$$-mixing condition. Both simulated and real data examples are used for illustration.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G08 Nonparametric regression and quantile regression 62J02 General nonlinear regression
fda (R)
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