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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)

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

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

Note: Type of Document - PDF; pages: 20. PDF document submitted via ftp
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Related research
Keywords: smoothing parameter; cubic spline; state-space model; irregular surveys.;

Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C5 - Mathematical and Quantitative Methods - - Econometric Modeling

This paper has been announced in the following NEP Reports:

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  1. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. David K. Backus & Patrick J. Kehoe, 1992. "International Evidence on the Historical Properties of Business Cycles," Working Papers 92-5, New York University, Leonard N. Stern School of Business, Department of Economics.
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. 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.
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  7. 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. [Downloadable!] (restricted)
    Other versions:
  8. 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. [Downloadable!] (restricted)
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  9. Juan J. Dolado & Miguel Sebastián & Javier Vallés, 1993. "Cyclical Patterns of the Spanish Economy," Banco de España Working Papers 9324, Banco de España.
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  10. Mark A. Wynne & Jahyeong Koo, 1997. "Business cycles under monetary union: EU and US business cycles compared," Working Papers 97-07, Federal Reserve Bank of Dallas. [Downloadable!]
  11. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de España Working Papers 0108, Banco de España. [Downloadable!]
  12. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
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  13. Carter, C.K. & Kohn, R., . "Semiparametric Bayesian inference for time series with mixed spectra," Statistics Working Paper _005, Australian Graduate School of Management.
  14. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de España Working Papers 0108, Banco de España. [Downloadable!]
  15. 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.
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  16. Juan J. Dolado & Miguel Sebastián & Javier Vallés, 1993. "Cyclical Patterns of the Spanish Economy," Banco de España Working Papers 9324, Banco de España.
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