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.

This paper deals with statistical inferences based on the generallized varying-coefficient models proposed by Hastic and Tibshirani (1993). Local polynomial regression techniques are used to estimate coefficient functions and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coeffiecients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covariates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation techniques involve solving hundreds of local likelihood equations. To reduce computation burden, a one-step Newton-Raphson estimator is proposed and implemented. We show that the resulting one-step procedure can save computational cost in an order of tens without deteriorating its performance, both asymptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.