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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)

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    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. 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.
    2. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
    3. 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.
    4. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Canova, Fabio, 1994. "Detrending and turning points," European Economic Review, Elsevier, vol. 38(3-4), pages 614-623, April.
    6. 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.
    7. Jaeger, Albert, 1994. "Mechanical Detrending by Hodrick-Prescott Filtering: A Note," Empirical Economics, Springer, vol. 19(3), pages 493-500.
    8. Lucas, Robert E., 1977. "Understanding business cycles," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 5(1), pages 7-29, January.
    9. 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.
    10. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
    11. David K. Backus & Patrick J. Kehoe, 1992. "International Evidence on the Historical Properties of Business Cycles," Working Papers 92-5, New York University, Leonard N. Stern School of Business, Department of Economics.
    12. 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.
    13. 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.
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