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Reconstructing dynamics from intertemporal economic data

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  • Venkatesh Bala

    (Department of Economics, McGill University, 855 Sherbrooke Street W., Montreal, Quebec H3A 2T7, CANADA)

Abstract

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.

Suggested Citation

  • Venkatesh Bala, 1997. "Reconstructing dynamics from intertemporal economic data," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 325-339.
    • Handle: RePEc:spr:joecth:v:9:y:1997:i:2:p:325-339
    Note: Received: April 25, 1994; revised version December 29, 1995
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