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

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

    (University of Auckland)

Registered author(s):

    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.

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    Paper provided by University of Auckland, Department of Economics in its series Reports with number 9602.

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    Handle: RePEc:wop:auecwp:9602
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    1. 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 231-47, July-Sept.
    2. 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.
    3. 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.
    4. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-18.
    5. 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 864-88, September.
    6. Canova, Fabio, 1994. "Detrending and turning points," European Economic Review, Elsevier, vol. 38(3-4), pages 614-623, April.
    7. 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.
    8. Lucas, Robert E., 1977. "Understanding business cycles," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 5(1), pages 7-29, January.
    9. 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.
    10. 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.
    11. Jaeger, Albert, 1994. "Mechanical Detrending by Hodrick-Prescott Filtering: A Note," Empirical Economics, Springer, vol. 19(3), pages 493-500.
    12. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
    13. Peter Brandner & Klaus Neusser, 1992. "Business cycles in open economies: Stylized facts for Austria and Germany," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 128(1), pages 67-87, March.
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