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Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter

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Author Info

  • Roberto Iannaccone

    (Istat)

  • Edoardo Otranto

    (DEIR-Università di Sassari)

Abstract

A widely used filter to extract a signal in a time series, in particular in the business cycle analysis, is the Hodrick-Prescott filter. The model that underlies the filter considers the data series as the sum of two unobserved component (signal and non signal) and a smoothing parameter which for quarterly series is set to a specified value. This paper proposes a generalization of the Hodrick-Prescott filter to a continuous time support, using the well-established relationship between cubic splines and state-space models. The spline formulation of the filter leads to a state space model with several practical advantages: first, the smoothing parameter can be either pre-specified or estimated as the other parameters in the model; second, the unobserved components can be modelled by the addition of particular ARIMA structures; lastly the model is capable of working in the presence of missing values or for irregular surveys. Monte Carlo experiments support these considerations.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0311002.

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Length: 20 pages
Date of creation: 07 Nov 2003
Date of revision:
Handle: RePEc:wpa:wuwpem:0311002

Note: Type of Document - PDF; pages: 20. PDF document submitted via ftp
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Web page: http://128.118.178.162

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Keywords: smoothing parameter; cubic spline; state-space model; irregular surveys.;

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References

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  1. Carter, C.K. & Kohn, R., . "Semiparametric Bayesian inference for time series with mixed spectra," Statistics Working Paper _005, Australian Graduate School of Management.
  2. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
  3. A. C. Harvey & Siem Jan Koopman, 2000. "Computing Observation Weights for Signal Extraction and Filtering," Econometric Society World Congress 2000 Contributed Papers 0888, Econometric Society.
  4. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
  5. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  6. Víctor Gómez & Agustín Maravall, 1998. "Seasonal Adjustment and Signal Extraction in Economic Time Series," Banco de Espa�a Working Papers 9809, Banco de Espa�a.
  7. Juan J. Dolado & Miguel Sebastián & Javier Vallés, 1993. "Ciclical patterns of the spanish economy," Investigaciones Economicas, Fundación SEPI, vol. 17(3), pages 445-473, September.
  8. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
  9. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. 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.
  11. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
  12. Cogley, Timothy, 2001. "Alternative definitions of the business cycle and their implications for business cycle models: A reply to Torben Mark Pederson," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1103-1107, August.
  13. Juan J. Dolado & Miguel Sebastián & Javier Vallés, 1993. "Cyclical Patterns of the Spanish Economy," Banco de Espa�a Working Papers 9324, Banco de Espa�a.
  14. 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.
  15. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  16. Mark A. Wynne & Jahyeong Koo, 1997. "Business cycles under monetary union: EU and US business cycles compared," Working Papers 9707, Federal Reserve Bank of Dallas.
  17. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  18. 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.
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