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

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  • Kaiser, Regina
  • Maravall, Agustin

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.

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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 21 (2005)
Issue (Month): 4 ()
Pages: 691-710

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Handle: RePEc:eee:intfor:v:21:y:2005:i:4:p:691-710

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Web page: http://www.elsevier.com/locate/ijforecast

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References

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  1. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  2. Robert F. Engle, 1978. "Estimating Structural Models of Seasonality," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 281-308 National Bureau of Economic Research, Inc.
  3. 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.
  4. Maravall, Agustin, 1988. "A note on minimum mean squared error estimation of signals with unit roots," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 589-593.
  5. David A. Pierce, 1978. "Seasonal adjustment when both deterministic and stochastic seasonality are present," Special Studies Papers 107, Board of Governors of the Federal Reserve System (U.S.).
  6. Pollock, D. S. G., 2000. "Trend estimation and de-trending via rational square-wave filters," Journal of Econometrics, Elsevier, vol. 99(2), pages 317-334, December.
  7. David A. Pierce, 1978. "Seasonal Adjustment When Both Deterministic and Stochastic Seasonality Are Present," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 242-280 National Bureau of Economic Research, Inc.
  8. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  9. Burridge, Peter & Wallis, Kenneth F, 1984. "Unobserved-Components Models for Seasonal Adjustment Filters," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 350-59, October.
  10. Morten O. Ravn & Harald Uhlig, 2002. "On adjusting the Hodrick-Prescott filter for the frequency of observations," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 371-375.
  11. Maravall, Agustin, 1985. "On Structural Time Series Models and the Characterization of Components," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 350-55, October.
  12. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
  13. Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
  14. 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.
  15. 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.
  16. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-64, July.
  17. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  18. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
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Citations

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Cited by:
  1. Agustín Maravall & Ana del Río, 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Banco de Espa�a Working Papers 0728, Banco de Espa�a.
  2. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, 09.
  3. Julio Roman, Juan Manuel, 2011. "The Hodrick-Prescott filter with priors: linear restrictions on HP filters," MPRA Paper 34202, University Library of Munich, Germany.
  4. 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.
  5. Tommaso Proietti, 2008. "Structural Time Series Models for Business Cycle Analysis," CEIS Research Paper 109, Tor Vergata University, CEIS, revised 10 Jul 2008.
  6. Terence C. Mills, 2013. "Constructing U.K. Core Inflation," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 32-52, April.
  7. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
  8. Agustín Maravall Herrero & Domingo Pérez Cañete, 2011. "Applying and interpreting model-based seasonal adjustment. The euro-area industrial production series," Banco de Espa�a Working Papers 1116, Banco de Espa�a.
  9. Proietti, Tommaso & Musso, Alberto, 2007. "Growth accounting for the euro area: a structural approach," Working Paper Series 0804, European Central Bank.
  10. Juan Manuel Julio, . "Data Revisions and the Output Gap," Borradores de Economia 642, Banco de la Republica de Colombia.
  11. Kamilya Tazhibayeva & Aasim M. Husain & Anna Ter-Martirosyan, 2008. "Fiscal Policy and Economic Cycles in Oil-Exporting Countries," IMF Working Papers 08/253, International Monetary Fund.

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