On The Spectral Properties Of Matrices Associated With Trend Filters
This 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.
Volume (Year): 26 (2010)
Issue (Month): 04 (August)
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- Lawrence J. Christiano & Terry J. Fitzgerald, 2003.
"The Band Pass Filter,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, 05.
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- Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, Junio.
- 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.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, Junio.
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