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A trend-cycle(-season) filter

  • Mohr, Matthias

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. JEL Classification: C13, C22, E32

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Paper provided by European Central Bank in its series Working Paper Series with number 0499.

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Date of creation: Jul 2005
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Handle: RePEc:ecb:ecbwps:20050499
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  1. Döpke, Jörg, 2004. "Real-time data and business cycle analysis in Germany," Discussion Paper Series 1: Economic Studies 2004,11, Deutsche Bundesbank, Research Centre.
  2. Kolasa, Marcin, 2005. "What drives productivity growth in the new EU member states? The case of Poland," Working Paper Series 0486, European Central Bank.
  3. Bouthevillain, C. & Van Den Dool, G. & Langenus, G. & Mohr, M. & Momigliano, S. & Tujula, M. & De Cos, P.H. & Cour-Thimann, Philippine, 2001. "Cyclically Adjusted Budget Balances: an Alternative Approach," Papers 77, Quebec a Montreal - Recherche en gestion.
  4. Ehrmann, Michael & Fratzscher, Marcel, 2005. "Communication and decision-making by central bank committees: different strategies, same effectiveness?," Working Paper Series 0488, European Central Bank.
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  7. Gruener Hans Peter & Hayo Bernd & Hefeker Carsten, 2009. "Unions, Wage Setting and Monetary Policy Uncertainty," The B.E. Journal of Macroeconomics, De Gruyter, vol. 9(1), pages 1-25, October.
  8. 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.
  9. Marco Del Negro & Frank Schorfheide, 2005. "Monetary policy analysis with potentially misspecified models," Working Papers 06-4, Federal Reserve Bank of Philadelphia.
  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. Michael Ehrmann & Marcel Fratzscher, 2007. "Communication by Central Bank Committee Members: Different Strategies, Same Effectiveness?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2-3), pages 509-541, 03.
  12. 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.
  13. Giovanni Lombardo & Alan Sutherland, 2005. " Computing Second-Order-Accurate Solutions for Rational Expectation Models Using Linear Solution Methods," CDMA Conference Paper Series 0504, Centre for Dynamic Macroeconomic Analysis.
  14. 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.
  15. 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.
  16. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2005. "Forecasting macroeconomic variables for the new member states of the European Union," Working Paper Series 0482, European Central Bank.
  17. 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.
  18. C�cile Denis & Kieran Mc Morrow & Werner R�ger, 2002. "Production function approach to calculating potential growth and output gaps - estimates for the EU Member States and the US," European Economy - Economic Papers 176, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
  19. 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 Publishing.
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