A shape metric for evolving time series models

Abstract

Most applications of Genetic Programming to time series modeling use a fitness measure for comparing potential solutions that treat each point in the time series independently. This non-temporal approach can lead to some potential solutions being given a relatively high fitness measure even though they do not correspond to the training data when the overall shape of the series is taken into account. This paper develops two fitness measures which emphasize the concept of shape when measuring the similarity between a training and evolved time series. One approach extends the root mean square error to higher dimensional derivatives of the series. The second approach uses a simplified derivative concept that describes shape in terms of positive, negative and zero slope.