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Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2009 (English)In: Studies in Nonlinear Dynamics and Econometrics, ISSN 1081-1826, Vol. 13, no 3Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2009. Vol. 13, no 3
Keyword [en]
time-series, signal extraction, cycles
URN: urn:nbn:se:kth:diva-18472ISI: 000266529700003ScopusID: 2-s2.0-67650912317OAI: diva2:336519
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-02-18Bibliographically approved

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Dermoune, AzzouzDjehiche, BoualemRahmania, Nadji
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