ABSTRACT
This paper addresses the problem of how to decide whether a time series comes from a deterministic dynamical system. At its root, this problem is ill-posed because any time series of finite length-even one that was generated by a deterministic process-is a possible realization of some random process. In practice, though, one usually has in mind some class of random processes such as linear dynamical systems with Gaussian white noise inputs, and it is worthwhile to pose the problem as deciding whether the time series is a plausible output of this class of random processes. A reasonable approach to this problem is to compute some statistic (or set of statistics) on the time series, and assess the likelihood that the computed values would come from the class of random systems under consideration.
