Abstract
This dissertation consists of 3 essays In the first essay, A Simple Variable Selection Technique for Nonlinear Models, written in cooperation with Timo Teräsvirta and Rolf Tschernig, I propose a variable selection method based on a polynomial expansion of the unknown regression function and an appropriate model selection criterion. The hypothesis of linearity is tested by a Lagrange multiplier test based on this polynomial expansion. If rejected, a kth order general polynomial is used as a base for estimating all submodels by ordinary least squares. The combination of regressors leading to the lowest value of the model selection criterion is selected. The second essay, Modelling and Forecasting Economic Time Series with Single Hidden-layer Feedforward Autoregressive Artificial Neural Networks, proposes an unified framework for artificial neural network modelling. Linearity is tested and the selection of regressors performed by the methodology developed in essay I. The number of hidden units is detected by a procedure based on a sequence of Lagrange multiplier (LM) tests. Serial correlation of errors and parameter constancy are checked by LM tests as well. A Monte-Carlo study, the two classical series of the lynx and the sunspots, and an application on the monthly S&P 500 index return series are used to demonstrate the performance of the overall procedure. In the third essay, Forecasting with Artificial Neural Network Models (in cooperation with Marcelo Medeiros), the methodology developed in essay II, the most popular methods for artificial neural network estimation, and the linear autoregressive model are compared by forecasting performance on 30 time series from different subject areas. Early stopping, pruning, information criterion pruning, cross-validation pruning, weight decay, and Bayesian regularization are considered. The findings are that 1) the linear models very often outperform the neural network ones and 2) the modelling approach to neural networks developed in this thesis stands up well with in comparison when compared to the other neural network modelling methods considered here.