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Generalised Fading Memory Learning in a Cobweb Model: some evidence

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  • Domenico Colucci
  • Vincenzo Valori

Abstract

We develop a learning rule that generalises the well known fading memory learning in the sense that the weights attached to the available time series data are not constant and are updated in light of the prediction error(s). The underlying idea is that confidence in the available data will be low when large errors have been realized (e.g. in times of higher volatility) and vice versa. A class of functional forms compatible with this idea is analysed in the context of a standard Cobweb model with boundedly rational agents. We study the problem of convergence to the perfect foresight equilibrium (both local and global) and give conditions that ensure the coexistence of different attractors. We refer to both experimental and numerical evidence to establish the possible range of application of the generalised fading memory learning

Suggested Citation

  • Domenico Colucci & Vincenzo Valori, 2004. "Generalised Fading Memory Learning in a Cobweb Model: some evidence," Computing in Economics and Finance 2004 272, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:272
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    References listed on IDEAS

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    1. Lovell, Michael C, 1986. "Tests of the Rational Expectations Hypothesis," American Economic Review, American Economic Association, vol. 76(1), pages 110-124, March.
    2. Hommes, Cars H., 1998. "On the consistency of backward-looking expectations: The case of the cobweb," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 333-362, January.
    3. Potzelberger, Klaus & Sogner, Leopold, 2003. "Stochastic equilibrium: learning by exponential smoothing," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1743-1770, August.
    4. Kirman, A., 1997. "Interaction and Markets," ASSET - Instituto De Economia Publica 166, ASSET (Association of Southern European Economic Theorists).
    5. Colucci, Domenico & Valori, Vincenzo, 2005. "Error learning behaviour and stability revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 371-388, March.
    6. Williams, Arlington W, 1987. "The Formation of Price Forecasts in Experimental Markets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 19(1), pages 1-18, February.
    7. Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, vol. 59(4), pages 401-426, October.
    8. Hey, John D., 1994. "Expectations formation: Rational or adaptive or ...?," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 329-349, December.
    9. Jensen, Roderick V. & Urban, Robin, 1984. "Chaotic price behavior in a non-linear cobweb model," Economics Letters, Elsevier, vol. 15(3-4), pages 235-240.
    10. Carl Chiarella & Xue-Zhong He & Peiyuan Zhu, 2003. "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers," Research Paper Series 108, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Hugh Kelley & Daniel Friedman, 2002. "Learning to Forecast Price," Economic Inquiry, Western Economic Association International, vol. 40(4), pages 556-573, October.
    12. repec:cup:macdyn:v:2:y:1998:i:3:p:287-321 is not listed on IDEAS
    13. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
    14. Artstein, Zvi, 1983. "Irregular cobweb dynamics," Economics Letters, Elsevier, vol. 11(1-2), pages 15-17.
    15. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
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    More about this item

    Keywords

    bounded rationality; learning dynamics; fading memory; nonlinear cobweb model.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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