A trend-cycle(-season) filter
AbstractThis 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
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by European Central Bank in its series Working Paper Series with number 0499.
Date of creation: Jul 2005
Date of revision:
Contact details of provider:
Postal: Postfach 16 03 19, Frankfurt am Main, Germany
Phone: +49 69 1344 0
Fax: +49 69 1344 6000
Web page: http://www.ecb.europa.eu/home/html/index.en.html
More information through EDIRC
Postal: Press and Information Division, European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany
Other versions of this item:JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-04 (All new papers)
- NEP-DGE-2005-10-04 (Dynamic General Equilibrium)
- NEP-ETS-2005-10-04 (Econometric Time Series)
- NEP-MAC-2005-10-04 (Macroeconomics)
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.:
- 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.
- Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
- 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.
- Grüner, Hans Peter & Hayo, Bernd & Hefeker, Carsten, 2005. "Unions, wage setting and monetary policy uncertainty," Working Paper Series 0490, European Central Bank.
- 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.
- 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.
- Lombardo, Giovanni & Sutherland, Alan, 2005.
"Computing second-order-accurate solutions for rational expectation models using linear solution methods,"
Working Paper Series
0487, European Central Bank.
- 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.
- 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.
- Cogley, Timothy & Sargent, Thomas J., 2005.
"The conquest of U.S. inflation: learning and robustness to model uncertainty,"
Working Paper Series
0478, European Central Bank.
- 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.
- Marco Del Negro & Frank Schorfheide, 2005.
"Monetary policy analysis with potentially misspecified models,"
2005-26, Federal Reserve Bank of Atlanta.
- Marco Del Negro & Frank Schorfheide, 2009. "Monetary Policy Analysis with Potentially Misspecified Models," American Economic Review, American Economic Association, vol. 99(4), pages 1415-50, September.
- Marco Del Negro & Frank Schorfheide, 2005. "Monetary policy analysis with potentially misspecified models," Working Papers 06-4, Federal Reserve Bank of Philadelphia.
- Marco Del Negro & Frank Schorfheide, 2008. "Monetary policy analysis with potentially misspecified models," Staff Reports 321, Federal Reserve Bank of New York.
- Del Negro, Marco & Schorfheide, Frank, 2005. "Monetary policy analysis with potentially misspecified models," Working Paper Series 0475, European Central Bank.
- Marco Del Negro & Frank Schorfheide, 2007. "Monetary Policy Analysis with Potentially Misspecified Models," NBER Working Papers 13099, National Bureau of Economic Research, Inc.
- Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
- Döpke, Jörg, 2004. "Real-time data and business cycle analysis in Germany," Discussion Paper Series 1: Economic Studies 2004,11, Deutsche Bundesbank, Research Centre.
- Bouthevillain, Carine & Cour-Thimann, Philippine & van de Dool, Gerrit & Hernández de Cos, Pablo & Langenus, Geert & Mohr, Matthias & Momigliano, Sandro & Tujula, Mika, 2001.
"Cyclically adjusted budget balances: an alternative approach,"
Working Paper Series
0077, European Central Bank.
- 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.
- 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 Monetary Affairs (DG ECFIN), European Commission.
- 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.
- 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.
- Paul de Grauwe & Francesco Paolo Mongelli, 2005.
"Endogeneities of Optimum Currency Areas: What brings Countries Sharing a Single Currency Closer together?,"
Working Papers de Economia (Economics Working Papers)
29, Departamento de Economia, Gestão e Engenharia Industrial, Universidade de Aveiro.
- De Grauwe, Paul & Mongelli, Francesco Paolo, 2005. "Endogeneities of optimum currency areas: what brings countries sharing a single currency closer together?," Working Paper Series 0468, European Central Bank.
- Kolasa, Marcin, 2005. "What drives productivity growth in the new EU member states? The case of Poland," Working Paper Series 0486, European Central Bank.
- Ehrmann, Michael & Fratzscher, Marcel, 2005. "Communication and decision-making by central bank committees: different strategies, same effectiveness?," Working Paper Series 0488, European Central Bank.
- 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.
- 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.
- 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.
- 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.
- Destefanis, Sergio & Mastromatteo, Giuseppe, 2012. "Assessing the reassessment: A panel analysis of the Lisbon Strategy," Economics Letters, Elsevier, vol. 115(2), pages 148-151.
- Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
- Golinelli, Roberto & Momigliano, Sandro, 2006. "Real-time determinants of fiscal policies in the euro area," Journal of Policy Modeling, Elsevier, vol. 28(9), pages 943-964, December.
- 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 and International Relations Area.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Official Publications).
If references are entirely missing, you can add them using this form.