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

  • Michele Berardi
  • Jaqueson K. Galimberti

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
Contact details of provider: Postal: Manchester M13 9PL
Phone: (0)161 275 4868
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Web page: http://www.socialsciences.manchester.ac.uk/subjects/economics/our-research/centre-for-growth-and-business-cycle-research/

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  1. Evans, G.W. & Honkapohja ,S. & Williams, N., 2005. "Generalized Stochastic Gradient Learning," Cambridge Working Papers in Economics 0545, Faculty of Economics, University of Cambridge.
  2. McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 119-139, February.
  3. 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.
  4. 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.
  5. 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.
  6. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  7. George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," CESifo Working Paper Series 1576, CESifo Group Munich.
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