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

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Listed:
  • J. J. Reeves
  • C. A. Blyth
  • C. M. Triggs
  • J. P. Small

    (University of Auckland)

Abstract

This paper proposes a novel derivation of the Hodrick-Prescott, Department of Economics (HP) minimisation problem which leads to a generalisation of the Hodrick-Prescott filter. The main result is the development of a new filter to extract a localised maximum likelihood estimate of the cycle from a series. This new filter, the Multivariate Normal Cyclical (MNC) filter makes only a very general assumption about the cyclical nature of the series. Unlike most other filters, it does not make any explicit assumption about the nature of the trend component of the series.

Suggested Citation

  • J. J. Reeves & C. A. Blyth & C. M. Triggs & J. P. Small, "undated". "The Hodrick-Prescott Filter, a Generalisation, and a New Procedure for Extracting an Empirical Cycle from a Series," Reports 9602, University of Auckland, Department of Economics.
    • Handle: RePEc:wop:auecwp:9602
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    References listed on IDEAS

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    1. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
    2. Peter Brandner & Klaus Neusser, 1992. "Business cycles in open economies: Stylized facts for Austria and Germany," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 128(1), pages 67-87, March.
    3. Backus, David K & Kehoe, Patrick J, 1992. "International Evidence of the Historical Properties of Business Cycles," American Economic Review, American Economic Association, vol. 82(4), pages 864-888, September.
    4. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    5. Simkins, Scott P., 1994. "Do real business cycle models really exhibit business cycle behavior?," Journal of Monetary Economics, Elsevier, vol. 33(2), pages 381-404, April.
    6. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    7. Kim, Kunhong & Buckle, R A & Hall, V B, 1994. "Key Features of New Zealand Business Cycles," The Economic Record, The Economic Society of Australia, vol. 70(208), pages 56-73, March.
    8. Canova, Fabio, 1994. "Detrending and turning points," European Economic Review, Elsevier, vol. 38(3-4), pages 614-623, April.
    9. Lucas, Robert E., 1977. "Understanding business cycles," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 5(1), pages 7-29, January.
    10. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    11. Kunhong Kim & A. Buckle & V. B. Hall, 1994. "Key Features of New Zealand Business Cycles," The Economic Record, The Economic Society of Australia, vol. 70(208), pages 56-72, March.
    12. Jaeger, Albert, 1994. "Mechanical Detrending by Hodrick-Prescott Filtering: A Note," Empirical Economics, Springer, vol. 19(3), pages 493-500.
    13. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 14(Spr), pages 3-18.
    14. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
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    Cited by:

    1. Velimir Šonje & Igeta Vrbanc, 2000. "Measuring the Similarities of Economic Developments in Central Europe: A Correlation between the Business Cycles of Germany, Hungary, the Czech Republic and Croatia," Working Papers 3, The Croatian National Bank, Croatia.
    2. Bernd Süssmuth, 2002. "National and Supranational Business Cycles (1960-2000): A multivariate description of central G7 and EURO15 NIPA aggregates," CESifo Working Paper Series 658, CESifo.
    3. Rómulo A.Chumacero & Francisco A.Gallego, 2002. "Trends and cycles in real-time," Estudios de Economia, University of Chile, Department of Economics, vol. 29(2 Year 20), pages 211-229, December.

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