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

Author

Listed:
  • 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.

Suggested Citation

  • Roberto Iannaccone & Edoardo Otranto, 2003. "Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter," Econometrics 0311002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0311002
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    References listed on IDEAS

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    More about this item

    Keywords

    smoothing parameter; cubic spline; state-space model; irregular surveys.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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