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

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  • 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.

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Bibliographic Info

Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 13 (2009)
Issue (Month): 3 (May)
Pages: 1-35

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Handle: RePEc:bpj:sndecm:v:13:y:2009:i:3:n:4

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  1. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," IZA Discussion Papers 1054, Institute for the Study of Labor (IZA).
  2. Schlicht, Ekkehart, 1984. "Seasonal Adjustment in a Stochastic Model," Munich Reprints in Economics 3371, University of Munich, Department of Economics.
  3. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(04), pages 988-1009, August.
  4. Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
  5. 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.
  6. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
  7. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-18.
  8. 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.
  9. 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.
  10. 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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Cited by:
  1. 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.

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