CRITICAL RECONSIDERATION OF PHASE SPACE EMBEDDING AND LOCAL NON-PARAMETRIC PREDICTION OF OZONE TIME SERIES

摘要

Phase space prediction is a feature selection method which tries to 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 prediction accuracy to that of the ozone data. In this instance there does not appear to be any advantage to applying the phase space approach to univariate time series.