Phase space reconstruction using input-output time series data

In this paper we suggest that an extension of a procedure recently proposed by Wayland et al. [Phys. Rev. Lett. 70, 580 (1993)] for recognizing determ inism in an autonomous time series can also be used as a diagnostic for det ermining an appropriate embedding dimension for driven ("input-output") sys tems. We compare the results of this extension to the results produced by t he extensions to the method of false nearest neighbors put forward by Rhode s and Morari [Proceedings of the American Control Conference, Seattle, edit ed by The American Automatic Control Council (IEEE, Piscataway, 1995)] and the method of averaged false nearest neighbors by Cao et al. [S1063-651X(99 )12510-8].