Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization
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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Volume (Year): 13 (2009)
Issue (Month): 3 (May)
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- 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).
- Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," Discussion Papers in Economics 304, University of Munich, Department of Economics.
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- Schlicht, Ekkehart, 1982. "Seasonal Adjustment in a Stochastic Model," Darmstadt Discussion Papers in Economics 25, Darmstadt University of Technology, Department of Law and Economics.
- Schlicht, Ekkehart, 1984. "Seasonal Adjustment in a Stochastic Model," Munich Reprints in Economics 3371, University of Munich, Department of Economics.
- Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
- 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.
- McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(04), pages 988-1009, August. Full references (including those not matched with items on IDEAS)
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