Critical Reconsideration of Phase Space Embedding and Local Non-Parametric Prediction of Ozone Time Series

Phase space prediction is a feature selection method which triesto exploit non-linear dynamics of an underlying system. We describe and offer a critical reconsideration of this approach,discuss questions of whether non-linear methods are justified by the data, and apply them to ozone time series from single locations. Our main objectives are to obtain air quality forecasts in order to provide public health warnings and to provide an insight into the dynamics of the underlying system.Interestingly, comparable linear data sets (surrogates)have very similar structure and give similar predictionaccuracy to that of the ozone data. In this instance theredoes not appear to be any advantage to applying the phasespace approach to univariate time series.