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)
|Contact details of provider:|| Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK|
Web page: http://journals.cambridge.org/jid_ECT
References listed on IDEAS
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.:
- 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.
- 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.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
- Tom Doan, . "CFFILTER: RATS procedure to perform band pass filter using Christiano-Fitzgerald method," Statistical Software Components RTS00034, Boston College Department of Economics.
- 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.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1247-1261_99. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.