<title>Time series prediction by estimating Markov probabilities through topology preserving maps</title>

Abstract

Topology preserving maps derived from neural network learning algorithms are well suited to approximate probability distributions from data sets. We use such algorithms to generate maps which allow the prediction of future events from a sample time series. Our approach relies on computing transition probabilities modeling the time series as a Markov process. Thus the technique can be applied both to stochastic as well as to deterministic chaotic data and also permits the computation of `error bars' for estimating the quality of predictions. We apply the method to the prediction of measured chaotic and noisy time series.