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A Trend-Cycle(-Season) Filter

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Author Info
Matthias Mohr (European Central Bank)

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Abstract

This paper proposes a new univariate method to decompose a time series into a trend, a cyclical and a seasonal component: the Trend-Cycle filter (TC filter) and its extension, the Trend-Cycle-Season filter (TCS filter). They can be regarded as extensions of the Hodrick-Prescott filter (HP filter). In particular, the stochastic model of the HP filter is extended by explicit models for the cyclical and the seasonal component. The introduction of a stochastic cycle improves the filter in three respects: first, trend and cyclical components are more consistent with the underlying theoretical model of the filter. Second, the end-of- sample reliability of the trend estimates and the cyclical component is improved compared to the HP filter since the pro-cyclical bias in end- of-sample trend estimates is virtually removed. Finally, structural breaks in the original time series can be easily accounted for.

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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 0508004.

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Length: 44 pages
Date of creation: 03 Aug 2005
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Handle: RePEc:wpa:wuwpem:0508004

Note: Type of Document - pdf; pages: 44
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Web page: http://129.3.20.41

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Related research
Keywords: economic cycles; time series; filtering; trend-cycle decomposition; seasonality;

Other versions of this item:

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Pete Richardson & Laurence Boone & Claude Giorno & Mara Meacci & David Rae & David Turner, 2000. "The Concept, Policy Use and Measurement of Structural Unemployment: Estimating a Time Varying NAIRU Across 21 OECD Countries," OECD Economics Department Working Papers 250, OECD, Economics Department. [Downloadable!]
  2. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2005. "Forecasting macroeconomic variables for the new member states of the European Union," Working Paper Series 482, European Central Bank. [Downloadable!]
  3. Lombardo, Giovanni & Sutherland, Alan, 2007. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 515-530, February. [Downloadable!] (restricted)
    Other versions:
  4. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Marcin Kolasa, 2005. "What drives productivity growth in the new EU member states? The case of Poland," Working Paper Series 486, European Central Bank. [Downloadable!]
  7. Michael Ehrmann & Marcel Fratzscher, 2005. "Communication and decision-making by central bank committees - different strategies, same effectiveness?," Working Paper Series 488, European Central Bank. [Downloadable!]
  8. Marco Del Negro & Frank Schorfheide, 2005. "Monetary policy analysis with potentially misspecified models," Working Paper 2005-26, Federal Reserve Bank of Atlanta. [Downloadable!]
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  9. Timothy Cogley & Thomas J. Sargent, 2005. "The conquest of US inflation: Learning and robustness to model uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 528-563, April. [Downloadable!] (restricted)
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  10. Paul De Grauwe & Francesco Paolo Mongelli, 2005. "Endogeneities of optimum currency areas - what brings countries sharing a single currency closer together?," Working Paper Series 468, European Central Bank. [Downloadable!]
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  11. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
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  12. Chantal Dupasquier & Alain Guay & Pierre St-Amant, 1997. "A Comparison of Alternative Methodologies for Estimating Potential Output and the Output Gap," Working Papers 97-5, Bank of Canada. [Downloadable!]
  13. Philippine Cour-Thimann & Pablo Hernandez Cos & Matthias F. Mohr & Mika Tujula & Carine Bouthevillain & Geert Langenus & Sandro Momigliano & Gerrit Van Den Dool, 2001. "Cyclically adjusted budget balances: an alternative approach," Working Paper Series 077, European Central Bank. [Downloadable!]
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  14. Hans Peter Grüner & Bernd Hayo & Carsten Hefeker, 2005. "Unions, wage setting and monetary policy uncertainty," Working Paper Series 490, European Central Bank. [Downloadable!]
  15. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. David Gruen & Tim Robinson & Andrew Stone, 2002. "Output Gaps in Real Time: Are They Reliable Enough to Use for Monetary Policy?," RBA Research Discussion Papers rdp2002-06, Reserve Bank of Australia. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department. [Downloadable!]
  2. Roberto Golinelli & Sandro Momigliano, 2006. "Real-time determinants of fiscal policies in the euro area: Fiscal rules, cyclical conditions and elections," Temi di discussione (Economic working papers) 609, Bank of Italy, Economic Research Department. [Downloadable!]
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