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On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates

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  • Tommaso Proietti

Abstract

The article explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick-Prescott (HP) filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener-Kolmogorov (WK) signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition.

Suggested Citation

  • Tommaso Proietti, 2009. "On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 186-208.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:186-208
    DOI: 10.1080/07474930802388025
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    1. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
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    9. Michael Artis & Massimiliano Marcellino & Tommaso Proietti, 2004. "Dating Business Cycles: A Methodological Contribution with an Application to the Euro Area," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(4), pages 537-565, September.
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    Cited by:

    1. Tommaso Proietti & Alberto Musso, 2012. "Growth accounting for the euro area," Empirical Economics, Springer, vol. 43(1), pages 219-244, August.
    2. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    3. Galimberti, Jaqueson K. & Moura, Marcelo L., 2016. "Improving the reliability of real-time output gap estimates using survey forecasts," International Journal of Forecasting, Elsevier, vol. 32(2), pages 358-373.
    4. Siliverstovs Boriss, 2013. "Dating Business Cycles in Historical Perspective: Evidence for Switzerland," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 661-679, October.
    5. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    6. Tommaso Proietti, 2009. "Structural Time Series Models for Business Cycle Analysis," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 9, pages 385-433, Palgrave Macmillan.
    7. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60, Edward Elgar Publishing.
    8. Michal Andrle, 2013. "What Is in Your Output Gap? Unified Framework & Decomposition into Observables," IMF Working Papers 2013/105, International Monetary Fund.
    9. Jaqueson K. Galimberti & Marcelo L. Moura, 2011. "Improving the reliability of real-time Hodrick-Prescott filtering using survey forecasts," Centre for Growth and Business Cycle Research Discussion Paper Series 159, Economics, The University of Manchester.

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    More about this item

    Keywords

    Bandpass filters; Kalman filter and Smoother; Revisions; Signal extraction;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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