Dynamics from multivariate time series

Multivariate time series data are common in experimental and industrial systems. If the generating system has nonlinear dynamics, we may be able to construct a model that reproduces the dynamics and can be used for control and other purposes. In principle, multivariate time series are not necessary for recovering dynamics: according to the embedding theorem, only one time series should be needed. However, for real data, then may be large gains in using all of the measurements. In this paper we examine the issues of how to use multiple data streams most effectively for modeling and prediction. For example, perhaps the data are redundant in that only a subset of the data streams is useful. And how should we embed the data, if indeed embedding is required at all? We show how these questions can be answered, and describe some numerical experiments which show that using multivariate time series can significantly improve predictability. We also demonstrate a somewhat surprising synchronization between different reconstructions. (C) 1998 Elsevier Science B.V.