Analysis and prediction of time series based on nonlinear regression models

Abstract

Time series prediction is one of the most important nonlinear regression problems in machine learning. The performance of the prediction models constructed to solve this problem, such as the network with Gaussian kernel functions, is estimated and analyzed through the generalization error bounds. Recently suggested data dependent generalization error bounds utilizing so called Rademacher complexities look quite promising, but only a limited number of experiential results are currently available because of the difficulty in computing the actual Rademacher complexities. In this thesis, we introduce the data dependent generalization error bounds which are in a quite practical form. We also describe how to calculate the Rademacher complexities to make the bounds to be used for a model selection in non-linear regression problems. Experiments using networks with Gaussian kernel functions on artificial and real time series data suggest a potential of the data dependent generalization error bounds for model selections.