Some Approaches to Nonlinear Modelling and Prediction

Abstract

This thesis contains two parts. The first part deals with dimension reduction in nonparametric regressions. In this part we propose to use different single-index models for observations in different regions of the sample space. This approach inherits the estimation efficiency of the single-index model in each region, and at the same time allows the global model to have multi-dimensionality in the sense of conventional dimension reduction. On the other hand, the model can be seen as an extension of the CART model and the piecewise linear model. The second part deals with nonlinear time series analysis. In this part, we modify the Whittle likelihood estimation (WLE) such that it is applicable to models in which the theoretical spectral density functions are only partially available. In particular, our modified WLE can be applied to most nonlinear regressive or autoregressive models with residuals following a moving average process.