Reconstructing dynamics from intertemporal economic data

This paper is concerned with the relationship between a continuous dynamical system and the trajectory generated by such a system. The main result provides necessary and sufficient conditions for an infinite data stream to be rationalized as the output of a continuous law of motion. The paper develops concepts of informativeness of a given set of intertemporal data and shows that informativeness is maximal when the data is chaotic. It also demonstrates that with probability one the sample paths from a non-trivial independent and identically distributed stochastic process cannot be rationalized as the output of a continuous deterministic system. Two impossibility results are discussed which show that even with an infinite amount of data the hypothesis that the data has been generated by a non-monotonic function cannot be ruled out. An application concerning the recovery of the excess demand function from a sequence of price observations from the tatonnement process is also given.