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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/cgbcr/dpcgbcr/dpcgbcr170.pdf
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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. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," University of Oregon Economics Department Working Papers 2005-17, University of Oregon Economics Department, revised 18 May 2008.
  2. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
  3. 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.
  4. McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 119-139, February.
  5. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  6. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta.
  7. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  8. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  9. 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.
  10. Margaritis, Dimitris, 1990. "A time-varying model of rational learning," Economics Letters, Elsevier, vol. 33(4), pages 309-314, August.
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Cited by:
  1. 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.
  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.

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