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Introduction aux modèles espace-état et au filtre de Kalman

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  • Matthieu Lemoine
  • Florian Pelgrin

Abstract

This article details the main concepts, problems and applications related to state-space models. We first present the general framework for these models and we, then, make explicit the algorithms used for the estimation, i.e. the Kalman filter and the EM algorithm. We, finally, analyse four applications : the decomposition of series into trend and cycle, the extraction of coincident economic indicators, the estimation of a time-varying equilibrium unemployment rate (TV-NAIRU) and the assessment of the informative content of the yield curve regarding future inflation.

Suggested Citation

  • Matthieu Lemoine & Florian Pelgrin, 2003. "Introduction aux modèles espace-état et au filtre de Kalman," Revue de l'OFCE, Presses de Sciences-Po, vol. 86(3), pages 203-229.
  • Handle: RePEc:cai:reofsp:reof_086_0203
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    1. Garbade, Kenneth & Wachtel, Paul, 1978. "Time variation in the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 4(4), pages 755-765, November.
    2. Robert J. Gordon, 1997. "The Time-Varying NAIRU and Its Implications for Economic Policy," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 11-32, Winter.
    3. Guilhem Bentoglio & Jacky Fayolle & Matthieu Lemoine, 2001. "Unité et pluralité du cycle européen," Revue de l'OFCE, Presses de Sciences-Po, vol. 78(3), pages 9-73.
    4. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    5. Mishkin, Frederic S., 1990. "What does the term structure tell us about future inflation?," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 77-95, January.
    6. Chopin, Nicolas & Pelgrin, Florian, 2004. "Bayesian inference and state number determination for hidden Markov models: an application to the information content of the yield curve about inflation," Journal of Econometrics, Elsevier, vol. 123(2), pages 327-344, December.
    7. Guay, A & St-Amant, P, 1996. "Do Mechanical Filters Provide a Good Approximation of Business Cycles?," Technical Reports 78, Bank of Canada.
    8. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    9. repec:spo:wpecon:info:hdl:2441/2130 is not listed on IDEAS
    10. Laurence Boone, 2000. "Comparing Semi-Structural Methods to Estimate Unobserved Variables: The HPMV and Kalman Filters Approaches," OECD Economics Department Working Papers 240, OECD Publishing.
    11. Kozicki, Sharon & Tinsley, P. A., 2001. "Term structure views of monetary policy under alternative models of agent expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 149-184, January.
    12. Tzavalis, Elias & Wickens, M. R., 1996. "Forecasting inflation from the term structure," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 103-122, May.
    13. Francis X. Diebold & Glenn D. Rudebusch, 1999. "Business Cycles: Durations, Dynamics, and Forecasting," Economics Books, Princeton University Press, edition 1, number 6636.
    14. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
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    Cited by:

    1. Éric Heyer & Frédéric Reynès & Henri Sterdyniak, 2005. "Variables observables et inobservables dans la théorie du taux de chômage d'équilibre. Une comparaison France/États-Unis," Revue économique, Presses de Sciences-Po, vol. 56(3), pages 593-603.
    2. Odile Chagny & Matthieu Lemoine, 2003. "Écart de production dans la zone euro. Une estimation par le filtre de Hodrick-Prescott multivarié," Revue de l'OFCE, Presses de Sciences-Po, vol. 86(3), pages 173-202.
    3. repec:spo:wpecon:info:hdl:2441/2128 is not listed on IDEAS
    4. Bationo, Rakissiwinde & Hounkpodote, Hilaire, 2009. "Estimation des changements des cours du café et du cacao: Filtre de Kalman, filtre de Hodrick-Prescott et modélisation à partir de processus markovien
      [Estimated Changes in Prices of Coffee and Coc
      ," MPRA Paper 26980, University Library of Munich, Germany, revised Nov 2010.
    5. Fathi, Elachhab, 2007. "Une analyse historiographique des causes du cycle économique en Tunisie," L'Actualité Economique, Société Canadienne de Science Economique, vol. 83(3), pages 359-397, septembre.
    6. Jean-Pierre Allegret & Alain Sand-Zantman, 2007. "Transmission des chocs et mécanismes d'ajustement dans le Mercosur," Revue de l'OFCE, Presses de Sciences-Po, vol. 101(2), pages 355-392.
    7. Allegret, Jean-Pierre & Sand-Zantman, Alain, 2010. "Processus d’intégration et coordination des politiques macroéconomiques dans le Mercosur : une approche en termes de cycles," L'Actualité Economique, Société Canadienne de Science Economique, vol. 86(2), pages 163-204, juin.
    8. repec:spo:wpecon:info:hdl:2441/2005 is not listed on IDEAS
    9. Lecarpentier-Moyal, Sylvie & Renou-Maissant, Patricia, 2007. "Analyse dynamique de la convergence des comportements de demande de monnaie en Europe," L'Actualité Economique, Société Canadienne de Science Economique, vol. 83(3), pages 321-357, septembre.

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