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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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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," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
  2. 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.
  3. McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 119-139, February.
  4. Thomas J. Sargent & Noah Williams, 2003. "Impacts of priors on convergence and escapes from Nash inflation," Working Paper 2003-14, Federal Reserve Bank of Atlanta.
  5. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
  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.
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