RECONSTRUCTING DYNAMICS FROM INTERTEMPORAL ECONOMIC DATA

This paper is concerned with the relationship between a continuous dyn amical system and the trajectory generated by such a system. The main result provides necessary and sufficient conditions for an infinite da ta stream to be rationalized as the output of a continuous law of moti on. The paper develops concepts of informativeness of a given set of i ntertemporal data and shows that informativeness is maximal when the d ata is chaotic. It also demonstrates that with probability one the sam ple paths from a non-trivial independent and identically distributed s tochastic process cannot be rationalized as the output of a continuous deterministic system. Two impossibility results are discussed which s how that even with an infinite amount of data the hypothesis that the data has been generated by a non-monotonic function cannot be ruled ou t. An application concerning the recovery of the excess demand functio n from a sequence of price observations from the tatonnement process i s also given.