Comparing random and deterministic time series

Summary This paper addresses the question of distinguishing the output of a stochastic process from that of a deterministic process. An impossibility theorem is described which states that time a series resulting from deterministic B-processes is observationally equivalent to, and hence indistinguishable from, the output of a continuous time Markov process on a finite number of states.This is an expanded version of a lecture presented at Cornell University in June, 1992 in a conference honoring Roy Radner on his 65th birthday. I would like to thank the organizers of this conference, especially Mukul Majumdar. The author is partially supported by a grant from the NSF.