| Nonlinear time series analysis has gained much attention in recent years due primarily to the fact that linear time series models have encountered various limitations in real applications and the development in nonparametric regression has established a solid foundation for nonlinear time series analysis. In this dissertation, polynomial spline smoothing is studied for nonlinear time series.;For univariate nonlinear time series, uniform confidence bands of a nonparametric prediction function are constructed using the polynomial spline method. As an application, after removing the environmental Kuznets curve trend effects, the impact of the economic intervention on environmental quality change is quantified for the United States and Japan, with different conclusions.;Application of non- and semiparametric regression techniques to high dimensional time series data have been hampered due to the lack of effective tools to address the "curse of dimensionality". There are essentially two approaches to circumvent this difficulty: function approximation and dimension reduction.;For the function approximation approach, the nonlinear additive autoregression (NAAR) model is examined. Under rather weak conditions, spline-backfitted kernel estimators of the component functions are proposed for weakly dependent samples that are both computationally expedient (so it is usable for analyzing very high dimensional time series), and theoretically reliable (so inference can be made on the component functions with confidence).;For the dimension reduction approach, a single-index prediction (SIP) model based on weakly dependent sample is studied. The single-index is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether or not the prediction function is a genuine single-index function. A polynomial spline estimator is proposed for the single-index prediction coefficients, and is shown to be root- n consistent and asymptotically normal. An iterative optimization routine is used which is sufficiently fast for the user to analyze large data sets of high dimension within seconds. Application of the proposed procedure to the river flow data of Iceland has yielded superior out-of-sample rolling forecasts. |
