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Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter

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  • Gebhard Flaig

Abstract

The HP filter is the most popular filter for extracting the trend and cycle components from an observed time series. Many researchers consider the smoothing parameter ë = 1600 as something like an universal constant. It is well known that the HP filter is an optimal filter under some restrictive assumptions, especially that the “cycle” is white noise. In this paper we show that one gets a good approximation of the optimal Wiener-Kolmogorov filter for autocorrelated cycle components by using the HP filter with a much higher smoothing parameter than commonly used. In addition, a new method - based on the properties of the differences of the estimated trend - is proposed for the selection of the smoothing parameter.

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File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2012/wp-cesifo-2012-05/cesifo1_wp3816.pdf
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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3816.

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Date of creation: 2012
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Handle: RePEc:ces:ceswps:_3816

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Related research

Keywords: Hodrick-Prescott filter; Wiener-Kolmogorov filter; smoothing parameter; trends; cycles;

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References

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  1. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(04), pages 988-1009, August.
  2. Harvey, Andrew C. & Delle Monache, Davide, 2009. "Computing the mean square error of unobserved components extracted by misspecified time series models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(2), pages 283-295, February.
  3. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 17(1-2), pages 207-231.
  4. 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, Elsevier, vol. 19(1-2), pages 253-278.
  5. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, Elsevier, vol. 18(1), pages 49-75, July.
  6. George E. P. Box & Steven Hillmer & George C. Tiao, 1979. "Analysis and Modeling of Seasonal Time Series," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 309-346 National Bureau of Economic Research, Inc.
  7. Gomez, Victor, 1999. "Three Equivalent Methods for Filtering Finite Nonstationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 17(1), pages 109-16, January.
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Cited by:
  1. Bloechl, Andreas, 2014. "Reducing the Excess Variability of the Hodrick-Prescott Filter by Flexible Penalization," Discussion Papers in Economics, University of Munich, Department of Economics 17940, University of Munich, Department of Economics.
  2. Willi Leibfritz & Horst Rottmann, 2013. "Fiscal Policy During Business Cycles in Developing Countries: The Case of Africa," CESifo Working Paper Series 4484, CESifo Group Munich.
  3. Willi Leibfritz & Gebhard Flaig, 2013. "Economic Growth in Africa: Comparing Recent Improvements with the "lost 1980s and early 1990s" and Estimating New Growth Trends," CESifo Working Paper Series 4215, CESifo Group Munich.

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