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A trend-cycle(-season) filter

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  • Mohr, Matthias

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. JEL Classification: C13, C22, E32

Suggested Citation

  • Mohr, Matthias, 2005. "A trend-cycle(-season) filter," Working Paper Series 499, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2005499
    Note: 79802
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    File URL: https://www.ecb.europa.eu//pub/pdf/scpwps/ecbwp499.pdf
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    References listed on IDEAS

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    Cited by:

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    3. 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.
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    5. 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).
    6. 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.
    7. Kristian Jönsson, 2017. "Restricted Hodrick–Prescott filtering in a state-space framework," Empirical Economics, Springer, vol. 53(3), pages 1243-1251, November.
    8. Dmitrij Celov & Mariarosaria Comunale, 2022. "Business Cycles in the EU: A Comprehensive Comparison Across Methods," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 99-146, Emerald Group Publishing Limited.
    9. repec:prg:jnlpep:v:preprint:id:667:p:1-19 is not listed on IDEAS
    10. 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.
    11. 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.
    12. Radovan Kovačević, 2018. "Structural And Cyclical Factors Of Serbia’S Current Account," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 63(217), pages 75-98, April – J.
    13. Hiroshi Yamada & Ruixue Du, 2018. "Some Results on ℓ 1 Polynomial Trend Filtering," Econometrics, MDPI, vol. 6(3), pages 1-10, July.
    14. Destefanis, Sergio & Mastromatteo, Giuseppe, 2012. "Assessing the reassessment: A panel analysis of the Lisbon Strategy," Economics Letters, Elsevier, vol. 115(2), pages 148-151.
    15. 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.
    16. 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; filtering; seasonality; time series; trend-cycle decomposition;
    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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