Smoothing Techniques for Prediction of Non-Linear Time Series

Abstract

We address the problem of non-linear modelling of time series and give a brief introduction to the method of state space reconstruction — embedding one-dimensional data into a higher-dimensional space. This method is based on the fundamental result in the area of chaotic time series, the Takens reconstruction theorem. Then we consider, among other non-linear methods of prediction, the kernel estimation of autoregression, and introduce a variation of this method. We apply it to an experimental time series and compare its performance with predictions by feed-forward neural networks as well as with fitting a local and a global linear autoregression.