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A Trend-Cycle(-Season) Filter

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  • Matthias Mohr

    (European Central Bank)

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.

Suggested Citation

  • Matthias Mohr, 2005. "A Trend-Cycle(-Season) Filter," Econometrics 0508004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0508004
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
    2. Comunale, Mariarosaria, 2017. "Dutch disease, real effective exchange rate misalignments and their effect on GDP growth in EU," Journal of International Money and Finance, Elsevier, vol. 73(PB), pages 350-370.
    3. Batini, Nicoletta & Di Serio, Mario & Fragetta, Matteo & Melina, Giovanni & Waldron, Anthony, 2022. "Building back better: How big are green spending multipliers?," Ecological Economics, Elsevier, vol. 193(C).
    4. 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.
    5. Mariarosaria Comunale & Dmitrij Celov, 2021. "Business cycles in the EU: A comprehensive comparison across methods," Bank of Lithuania Discussion Paper Series 26, Bank of Lithuania.
    6. Albulene Kastrati & Geoff Pugh & Valentin Toci, 2017. "Output Gap In Transition Economies Using Unobserved Component Method: The Case Of Czech Republic, Estonia And Kosovo," Economic Thought and Practice, Department of Economics and Business, University of Dubrovnik, vol. 26(2), pages 477-500, december.
    7. 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.
    8. Radovan Kovačević, 2018. "Structural And Cyclical Factors Of Serbia’S Current Account," Economic Annals, Faculty of Economics, University of Belgrade, vol. 63(217), pages 75-98, April – J.
    9. Styliani Christodoulopoulou, 2014. "The effect of currency unions on business cycle correlations: the EMU case," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 177-222, May.
    10. Destefanis, Sergio & Mastromatteo, Giuseppe, 2012. "Assessing the reassessment: A panel analysis of the Lisbon Strategy," Economics Letters, Elsevier, vol. 115(2), pages 148-151.
    11. Anusha, "undated". "Evaluating reliability of some symmetric and asymmetric univariate filters," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2015-030, Indira Gandhi Institute of Development Research, Mumbai, India.
    12. William Gatt & Owen Grech, "undated". "An assessment of the Maltese housing market," CBM Policy Papers PP/02/2016, Central Bank of Malta.

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    More about this item

    Keywords

    economic cycles; time series; filtering; trend-cycle decomposition; seasonality;
    All these keywords.

    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; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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