Multiple Time Series and Attractor Reconstructions

Many experiments have the ability to record more than one time series of data simultaneously. We explore two issues that are present when multiple time series are used to reconstruct attractors which are not present in the case of one time series. First, we show that there is an algorithmic approach to false nearest neighbors that naturally extends the established, one‐series method. Second, the question of redundant information in two or more time series is a new issue and we show that the typical approach of mutual information can lead to erroneous results. The correct approach is a statistic that tests for the existence of a function which leads to the correct results.