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Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization

Author

Listed:
  • Dermoune Azzouz

    (Université des Sciences et Technologies de Lille 1)

  • Djehiche Boualem

    (Royal Institute of Technology)

  • Rahmania Nadji

    (Université des Sciences et Technologies de Lille 1)

Abstract

The univariate Hodrick-Prescott filter depends on the noise-to-signal ratio that acts as a smoothing parameter. We first propose an optimality criterion for choosing the best smoothing parameters. We show that the noise-to-signal ratio is the unique minimizer of this criterion, when we use an orthogonal parametrization of the trend, whereas it is not the case when an initial-value parametrization of the trend is applied. We then propose a multivariate extension of the filter and show that there is a whole class of positive definite matrices that satisfy a similar optimality criterion, when we apply an orthogonal parametrization of the trend.

Suggested Citation

  • Dermoune Azzouz & Djehiche Boualem & Rahmania Nadji, 2009. "Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-35, May.
    • Handle: RePEc:bpj:sndecm:v:13:y:2009:i:3:n:4
    DOI: 10.2202/1558-3708.1656
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    References listed on IDEAS

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    1. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," IZA Discussion Papers 1054, Institute of Labor Economics (IZA).
    2. Razzak, W., 1997. "The Hodrick-Prescott technique: A smoother versus a filter: An application to New Zealand GDP," Economics Letters, Elsevier, vol. 57(2), pages 163-168, December.
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    4. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    5. Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
    6. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 14(Spr), pages 3-18.
    7. Fabio Araujo & Marta Baltar Moreira Areosa & José Alvaro Rodrigues Neto, 2003. "r-filters: a Hodrick-Prescott Filter Generalization," Working Papers Series 69, Central Bank of Brazil, Research Department.
    8. Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
    9. Reeves Jonathan J. & Blyth Conrad A. & Triggs Christopher M. & Small John P., 2000. "The Hodrick-Prescott Filter, a Generalization, and a New Procedure for Extracting an Empirical Cycle from a Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(1), pages 1-17, April.
    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. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
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    Cited by:

    1. Dermoune, Azzouz & Preda, Cristian, 2017. "Parametrizations, fixed and random effects," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 162-176.
    2. Dermoune, Azzouz & Rahmania, Nadji & Wei, Tianwen, 2012. "General linear mixed model and signal extraction problem with constraint," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 311-321.
    3. Martin Boďa & Mariana Považanová, 2023. "How credible are Okun coefficients? The gap version of Okun’s law for G7 economies," Economic Change and Restructuring, Springer, vol. 56(3), pages 1467-1514, June.

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