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A note on exact correspondences between adaptive learning algorithms and the Kalman filter

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  • Michele Berardi
  • Jaqueson K. Galimberti

Abstract

Digressing into the origins of the two main algorithms considered in the literature of adaptive learning, namely Least Squares (LS) and Stochastic Gradient (SG), we found a connection between their non-recursive forms and their interpretation within a state-space unifying framework. Based on such connection, we extend the correspondence between the LS and the Kalman filter recursions to a formulation with time-varying gains of the former, and also present a similar correspondence for the case of the SG. Our correspondences hold exactly, in a computational implementation sense, and we discuss how they relate to previous approximate correspondences found in the literature.

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File URL: http://www.socialsciences.manchester.ac.uk/medialibrary/cgbcr/discussionpapers/dpcgbcr170.pdf
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Bibliographic Info

Paper provided by Economics, The Univeristy of Manchester in its series Centre for Growth and Business Cycle Research Discussion Paper Series with number 170.

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Length: 18 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:man:cgbcrp:170

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  1. Evans, G.W. & Honkapohja, S., 1998. "Stochastic Gradient Learning in the Cobweb Model," University of Helsinki, Department of Economics 438, Department of Economics.
  2. Margaritis, Dimitris, 1990. "A time-varying model of rational learning," Economics Letters, Elsevier, vol. 33(4), pages 309-314, August.
  3. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
  4. Wiliam Branch & George W. Evans, 2005. "A Simple Recursive Forecasting Model," University of Oregon Economics Department Working Papers 2005-3, University of Oregon Economics Department, revised 01 Feb 2005.
  5. Michele Berardi & Jaqueson K. Galimberti, 2012. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Centre for Growth and Business Cycle Research Discussion Paper Series 170, Economics, The Univeristy of Manchester.
  6. Bullard, James, 1992. "Time-varying parameters and nonconvergence to rational expectations under least squares learning," Economics Letters, Elsevier, vol. 40(2), pages 159-166, October.
  7. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
  8. Thomas J. Sargent & Noah William, 2005. "Impacts of Priors on Convergence and Escapes from Nash Inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April.
  9. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  10. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," CESifo Working Paper Series 1576, CESifo Group Munich.
  11. Christopher A. Sims & Tao Zha, 2005. "Were There Regime Switches in U.S. Monetary Policy?," Working Papers 92, Princeton University, Department of Economics, Center for Economic Policy Studies..
  12. McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 119-139, February.
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Cited by:
  1. Michele Berardi & Jaqueson K. Galimberti, 2012. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Centre for Growth and Business Cycle Research Discussion Paper Series 170, Economics, The Univeristy of Manchester.
  2. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the initialization of adaptive learning algorithms: A review of methods and a new smoothing-based routine," Centre for Growth and Business Cycle Research Discussion Paper Series 175, Economics, The Univeristy of Manchester.
  3. Michele Berardi & Jaqueson K. Galimberti, 2012. "On the plausibility of adaptive learning in macroeconomics: A puzzling conflict in the choice of the representative algorithm," Centre for Growth and Business Cycle Research Discussion Paper Series 177, Economics, The Univeristy of Manchester.

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