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

Dermoune Azzouz (), Boualem Djehiche and Nadji Rahmania
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Dermoune Azzouz: Université des Sciences et Technologies de Lille 1

Studies in Nonlinear Dynamics & Econometrics, 2009, vol. 13, issue 3, 35

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.

Date: 2009
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DOI: 10.2202/1558-3708.1656

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