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The Hodrick-Prescott Filter, a Generalization, and a New Procedure for Extracting an Empirical Cycle from a Series

Author

Listed:
  • Reeves Jonathan J.

    (Queen’s University)

  • Blyth Conrad A.

    (The University of Auckland)

  • Triggs Christopher M.

    (The University of Auckland)

  • Small John P.

    (The University of Auckland)

Abstract

This paper proposes a novel derivation of the Hodrick-Prescott (HP) minimization problem which leads to a generalization of the Hodrick-Prescott filter. The main result is the development of a new filter to extract a localized maximum-likelihood estimate of the cycle from a series. This new filter, the multivariate normal cyclical (MNC) filter, makes only a general assumption about the cyclical nature of the series. The output from this filtering procedure is from a nonlinear optimization routine.

Suggested Citation

  • Reeves Jonathan J. & Blyth Conrad A. & Triggs Christopher M. & Small John P., 2000. "The Hodrick-Prescott Filter, a Generalization, and a New Procedure for Extracting an Empirical Cycle from a Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(1), pages 1-17, April.
    • Handle: RePEc:bpj:sndecm:v:4:y:2000:i:1:n:1
    DOI: 10.2202/1558-3708.1052
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    Cited by:

    1. Dermoune Azzouz & Djehiche Boualem & Rahmania Nadji, 2009. "Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-35, May.
    2. Luis Gonzalo Llosa & Shirley Miller, 2004. "Using Additional Information in Estimating the Output Gap in Peru: a Multivariate Unobserved Component Approach," Money Affairs, CEMLA, vol. 0(1), pages 57-82, January-J.
    3. Arby, Muhammad Farooq, 2001. "Long-run trend, Business Cycle & Short-run shocks in real GDP," MPRA Paper 4929, University Library of Munich, Germany.
    4. Iqbal Syed & Daniel Melser, 2008. "Prices over the Product Life Cycle: An Empirical Analysis," Discussion Papers 2008-25, School of Economics, The University of New South Wales.
    5. Martin Boďa & Mariana Považanová, 2023. "How credible are Okun coefficients? The gap version of Okun’s law for G7 economies," Economic Change and Restructuring, Springer, vol. 56(3), pages 1467-1514, June.
    6. Melser, Daniel & Syed, Iqbal, 2007. "Life Cycle Pricing and the Measurement of Inflation," MPRA Paper 16722, University Library of Munich, Germany, revised 07 Jul 2008.
    7. Petr Jakubík, 2006. "Does Credit Risk Vary with Economic Cycles? The Case of Finland," Working Papers IES 2006/11, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2006.
    8. Skikiewicz Robert, 2013. "Interest rates and changes in zloty deposits of households in Poland," Folia Oeconomica Stetinensia, Sciendo, vol. 13(1), pages 95-107, December.
    9. Guerrero, Victor M., 2007. "Time series smoothing by penalized least squares," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1225-1234, July.

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