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Estimation of the business cycle: A modified Hodrick-Prescott filter


  • Regina Kaiser

    () (Departamento de Estadística y Econometría, Universidad Carlos III de Madrid, calle Madrid 126, E-28903 Getafe , Spain Servicio de Estudios - Banco de Espa na, Alcalá 50, E-28014 Madrid, Spain)

  • Agustín Maravall

    () (Departamento de Estadística y Econometría, Universidad Carlos III de Madrid, calle Madrid 126, E-28903 Getafe , Spain Servicio de Estudios - Banco de Espa na, Alcalá 50, E-28014 Madrid, Spain)


Hodrick-Prescott (HP) filtering of (most often, seasonally adjusted) quarterly series is analysed. Some of the criticism to the filter are adressed. It is seen that, while filtering strongly affects autocorrelations, it has little effect on crosscorrelations. It is argued that the criticism that HP filtering induces a spurious cycle in the series is unwarranted. The filter, however, presents two serious drawbacks: First, poor performance at the end periods, due to the size of the revisions in preliminary estimators, and, second, the amount of noise in the cyclical signal, which seriously disturbs its interpretation. We show how the addition of two model-based features (in particular, applying the filter to the series extended with proper ARIMA forecasts and backcasts, and using as input to the filter the trend-cycle component instead of the seasonally adjusted series) can considerably improve the filter performance. Throughout the discussion, we use a computationally and analytically convenient alternative derivation of the HP filter, and illustrate the results with an example consisting of 4 Spanish economic indicators.

Suggested Citation

  • Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
  • Handle: RePEc:spr:specre:v:1:y:1999:i:2:p:175-206

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    Time series; optimal filtering; trends; seasonality; economic cycles;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles


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