On The Spectral Properties Of Matrices Associated With Trend Filters
AbstractThis note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the circulant and the generalized tau. These results are used to characterize the properties of a smoother in terms of an approximate eigen-decomposition of the associated smoothing matrix.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 26 (2010)
Issue (Month): 04 (August)
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Other versions of this item:
- Luati, Alessandra & Proietti, Tommaso, 2008. "On the Spectral Properties of Matrices Associated with Trend Filters," MPRA Paper 11502, University Library of Munich, Germany.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band Pass Filter,"
NBER Working Papers
7257, National Bureau of Economic Research, Inc.
- Estela Bee Dagum & Alessandra Luati, 2002. "A linear transformation and its properties with special applications in time series filtering," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
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