A Maximum Entropy Approach for Estimating Nonlinear Dynamic Models

  • Amos Golan
Part of the Fundamental Theories of Physics book series (FTPH, volume 105)

Abstract

Given the objective of estimating the unknown parameters of a finite (and relatively small) data set, generated by some (possibly nonlinear) dynamic discrete time process, it is common to use a Kalman filter Maximum Likelihood (ML) approach, ML-type estimators or more recently a GMM (Imbens, Spady and Johnson, 1998) or BMOM (Zellner 1997, Tobias and Zellner 1997) estimators. All of the above ML-type methods (except the BMOM) require some distributional assumptions while the moment-type estimators require some data (or assumptions) on the moments of the underlying distribution that generated the data. Recently, Golan, Judge and Miller (1996) and Golan, Judge and Karp (1996) developed a Maximum Entropy (ME) framework for estimating dynamic models without distributional assumptions. In this paper the above ME formulation is extended for estimating nonlinear (chaotic) dynamic models. Under this new formulation, one views the errors as another set of unknown parameters to be estimated. Thus, for any data set, the estimation problem is ill-posed (under-determined) where the number of unknowns is always greater than the number of data points and therefore the ME approach is a natural way to estimate the parameters. After developing the basic primal entropy model, a computationally efficient dual, unconstrained approach is developed. Under this dual method, the optimization is done with respect to the Lagrange multipliers associated with each observation. The dual is also used to contrast this ME approach with the more traditional ML-type estimators. Statistics and inference procedures are developed as well. Monte Carlo and empirical results for estimating the parameters of noisy, chaotic systems are presented as well.

Keywords

information maximum entropy nonlinear dynamic models 

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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Amos Golan
    • 1
  1. 1.American UniversityUSA

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