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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.

Suggested Citation

  • 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.
  • Handle: RePEc:man:cgbcrp:170
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    1. Thomas J. Sargent & Noah Williams, 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.
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    3. Berardi, Michele & Galimberti, Jaqueson K., 2013. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Economics Letters, Elsevier, vol. 118(1), pages 139-142.
    4. 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.
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    6. Margaritis, Dimitris, 1990. "A time-varying model of rational learning," Economics Letters, Elsevier, vol. 33(4), pages 309-314, August.
    7. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
    8. 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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    1. repec:eee:dyncon:v:78:y:2017:i:c:p:26-53 is not listed on IDEAS
    2. Berardi, Michele & Galimberti, Jaqueson K., 2013. "A note on exact correspondences between adaptive learning algorithms and the Kalman filter," Economics Letters, Elsevier, vol. 118(1), pages 139-142.
    3. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    4. Michele Berardi & Jaqueson K Galimberti, 2017. "Smoothing-based Initialization for Learning-to-Forecast Algorithms," KOF Working papers 17-425, KOF Swiss Economic Institute, ETH Zurich.
    5. Berardi, Michele & Galimberti, Jaqueson K., 2017. "On the initialization of adaptive learning in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 26-53.
    6. Christina Strobach & Carin van der Cruijsen, 2015. "The formation of European inflation expectations: One learning rule does not fit all," DNB Working Papers 472, Netherlands Central Bank, Research Department.
    7. Singleton, Carl & Schaefer, Daniel, 2015. "Unemployment and econometric learning," MPRA Paper 63162, University Library of Munich, Germany.
    8. 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.
    9. 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.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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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