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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 University of Manchester.
    • Handle: RePEc:man:cgbcrp:170
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    1. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Galimberti Jaqueson K., 2024. "Initial Beliefs Uncertainty," The B.E. Journal of Macroeconomics, De Gruyter, vol. 24(1), pages 45-96, January.
    4. Berardi, Michele & Galimberti, Jaqueson K., 2017. "Empirical calibration of adaptive learning," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 219-237.
    5. André Marine Charlotte & Dai Meixing, 2018. "Learning, robust monetary policy and the merit of precaution," The B.E. Journal of Macroeconomics, De Gruyter, vol. 18(2), pages 1-20, June.
    6. Marine Charlotte André & Meixing Dai, 2015. "Central bank accountability under adaptive learning," Working Papers of BETA 2015-32, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. 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.
    8. Berardi, Michele & Galimberti, Jaqueson K., 2019. "Smoothing-Based Initialization For Learning-To-Forecast Algorithms," Macroeconomic Dynamics, Cambridge University Press, vol. 23(3), pages 1008-1023, April.
    9. Berardi, Michele, 2019. "A probabilistic interpretation of the constant gain algorithm," MPRA Paper 94023, University Library of Munich, Germany.
    10. Schaefer, Daniel & Singleton, Carl, 2018. "Unemployment and econometric learning," Research in Economics, Elsevier, vol. 72(2), pages 277-296.
    11. Galimberti, Jaqueson K., 2019. "An approximation of the distribution of learning estimates in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 29-43.
    12. 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 University of Manchester.
    13. Michele Berardi, 2020. "A probabilistic interpretation of the constant gain learning algorithm," Bulletin of Economic Research, Wiley Blackwell, vol. 72(4), pages 393-403, October.
    14. 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 University of Manchester.

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    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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