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Combining filter design with model based filtering (with an application to business cycle estimation)

Author

Listed:
  • Regina Kaiser

    (Universidad Carlos III de Madrid)

  • Agustín Maravall

    (Banco de España)

Abstract

Filters used to estimate unobserved components in time series are often designed on a priori grounds, so as to capture the frequencies associated with the component. A limitation of these filters is that they may yield spurious results. The danger can be avoided if the so called ARIMA model based (AMB) procedure is used to derive the filter. However, parsimony of ARIMA models typically implies little resolution in terms of the detection of hidden components. It would be desirable to combine a higher resolution with consistency with the structure of the observed series. We show first that for a large class of a priori designed filters, an AMB interpretation is always possible. Using this result, proper convolution of AMB filters can produce richer decompositions of the series that incorporate a priori desired features for the components, and fully respect the ARIMA model for the observed series. (Hence no additional parameter needs to be estimated.) The procedure is discussed in detail in the context of business cycle estimation by means of the Hodrick Prescott filter applied to a seasonally adjusted series or a trend cycle component.

Suggested Citation

  • Regina Kaiser & Agustín Maravall, 2004. "Combining filter design with model based filtering (with an application to business cycle estimation)," Working Papers 0417, Banco de España.
    • Handle: RePEc:bde:wpaper:0417
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    Citations

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    Cited by:

    1. 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.
    2. McElroy Tucker S. & Maravall Agustin, 2014. "Optimal Signal Extraction with Correlated Components," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 237-273, July.
    3. Tommaso Proietti & Alberto Musso, 2012. "Growth accounting for the euro area," Empirical Economics, Springer, vol. 43(1), pages 219-244, August.
    4. Guy Mélard, 2016. "On some remarks about SEATS signal extraction," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 53-98, March.
    5. Agustín Maravall Herrero & Domingo Pérez Cañete, 2011. "Applying and interpreting model-based seasonal adjustment. The euro-area industrial production series," Working Papers 1116, Banco de España.
    6. Kamilya Tazhibayeva & Mr. Aasim M. Husain & Anna Ter-Martirosyan, 2008. "Fiscal Policy and Economic Cycles in Oil-Exporting Countries," IMF Working Papers 2008/253, International Monetary Fund.
    7. Maria Gadea & Ana Gómez-Loscos & Antonio Montañés, 2012. "Cycles inside cycles: Spanish regional aggregation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(4), pages 423-456, December.
    8. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    9. Julio Roman, Juan Manuel, 2011. "The Hodrick-Prescott filter with priors: linear restrictions on HP filters," MPRA Paper 34202, University Library of Munich, Germany.
    10. Juan Manuel Julio, 2011. "Data Revisions and the Output Gap," Borradores de Economia 642, Banco de la Republica de Colombia.
    11. Terence C. Mills, 2013. "Constructing U.K. Core Inflation," Econometrics, MDPI, vol. 1(1), pages 1-21, April.
    12. Dias, Maria Helena Ambrosio & Dias, Joilson, 2010. "Measuring the Cyclical Component of a Time Series: a New Proposed Methodology," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(1), October.
    13. 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.
    14. Musso, Alberto & Proietti, Tommaso, 2007. "Growth accounting for the euro area: a structural approach," Working Paper Series 804, European Central Bank.
    15. Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    16. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    17. 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.
    18. Peña, Daniel, 2020. "Agustín Maravall: An interview with the International Journal of Forecasting," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1241-1251.
    19. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    20. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    21. Acevedo Rueda, Rafael Alexis & Mora Mora, José U. & Harmath Fernández, Pedro Alexander, 2012. "La brecha del producto y el producto potencial en Venezuela: una estimación SVAR [Output Gap and Potential GDP in Venezuela: A SVAR Estimation]," MPRA Paper 58691, University Library of Munich, Germany, revised 2013.

    More about this item

    Keywords

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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