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Adaptive Learning with Nonlinear Dynamics Driven by Dependent Processes

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  • Kuan, Chung-Ming
  • White, Halbert

Abstract

The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. The authors draw on previous work by H. J. Kushner and D. S. Clark to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning. Copyright 1994 by The Econometric Society.

Suggested Citation

  • Kuan, Chung-Ming & White, Halbert, 1994. "Adaptive Learning with Nonlinear Dynamics Driven by Dependent Processes," Econometrica, Econometric Society, vol. 62(5), pages 1087-1114, September.
  • Handle: RePEc:ecm:emetrp:v:62:y:1994:i:5:p:1087-1114
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    Cited by:

    1. Chen Xiaohong & White Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-55, April.
    2. Atanas Christev, 2006. "Learning Hyperinflations," Computing in Economics and Finance 2006 475, Society for Computational Economics.
    3. Barucci, Emilio & Landi, Leonardo, 1996. "Speculative dynamics with bounded rationality learning," European Journal of Operational Research, Elsevier, vol. 91(2), pages 284-300, June.
    4. Heinemann, Maik, 2000. "Adaptive learning of rational expectations using neural networks," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 1007-1026, June.
    5. Pastorello, Sergio & Patilea, Valentin & Renault, Eric, 2003. "Iterative and Recursive Estimation in Structural Nonadaptive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 449-482, October.
    6. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
    7. Ulrich Horst & Jan Wezelburger, 2006. "Non-ergodic Behavior in a Financial Market with Interacting Investors," 2006 Meeting Papers 229, Society for Economic Dynamics.
    8. Guidolin, Massimo & Timmermann, Allan, 2007. "Properties of equilibrium asset prices under alternative learning schemes," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 161-217, January.
    9. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    10. Gregoir, Stephane & Weill, Pierre-Olivier, 2007. "Restricted perception equilibria and rational expectation equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 81-109, January.
    11. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
    12. Eric Ghysels & Norman R. Swanson & Myles Callan, 2002. "Monetary Policy Rules with Model and Data Uncertainty," Southern Economic Journal, Southern Economic Association, vol. 69(2), pages 239-265, October.
    13. Timothy Kam, 2004. "Two-sided Learning and Optimal Monetary Policy in an Open Economy Model," Economics Discussion / Working Papers 04-07, The University of Western Australia, Department of Economics.
    14. Peter Woehrmann & Willi Semmler & Martin Lettau, "undated". "Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models," IEW - Working Papers 225, Institute for Empirical Research in Economics - University of Zurich.
    15. Heinemann, Maik & Lange, Carsten, 1997. "Modellierung von Preiserwartungen durch neuronale Netze," Hannover Economic Papers (HEP) dp-203, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    16. Evans, George W. & Honkapohja, Seppo, 1998. "Convergence of learning algorithms without a projection facility," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 59-86, August.
    17. Flam, Sjur Didrik, 1996. "Approaches to economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1505-1522.

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