Interpretation of the Effects of Filtering Integrated Time Series
We resort to a rigorous definition of spectrum of an integrated time series in order to characterise the implications of applying linear filters to such series. We conclude that in the presence of integrated series the transfer function of the filters has exactly the same interpretation as in the covariance stationary case, contrary to what many authors suggest. This disagreement leads to different conclusions regarding the link of the original fluctuations with the transformed fluctuations in the time series data, embodied in various unjustified criticisms to the application of detrending filters. Despite this, and given the frequency domain characteristics of filtered macroeconomic integrated series, we acknowledge that the choice of a particular detrending filter is far from being a neutral task.
|Date of creation:||21 Sep 2007|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-73, July.
- Alain Guay & Pierre Saint-Amant, 2005.
"Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?,"
Annals of Economics and Statistics,
GENES, issue 77, pages 133-155.
- Alain Guay & Pierre St-Amant, 1997. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Cahiers de recherche CREFE / CREFE Working Papers 53, CREFE, Université du Québec à Montréal.
- Velasco, Carlos, 1998.
"Non-stationary log-periodogram regression,"
DES - Working Papers. Statistics and Econometrics. WS
4554, Universidad Carlos III de Madrid. Departamento de Estadística.
- Robert J. Hodrick & Edward Prescott, 1981.
"Post-War U.S. Business Cycles: An Empirical Investigation,"
451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
- 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.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc.
- Tom Doan, . "CFFILTER: RATS procedure to perform band pass filter using Christiano-Fitzgerald method," Statistical Software Components RTS00034, Boston College Department of Economics.
- João Valle e Azevedo, 2007.
"Exact Limit of the Expected Periodogram in the Unit-Root case,"
w200713, Banco de Portugal, Economics and Research Department.
- Valle e Azevedo, João, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root Case," MPRA Paper 6553, University Library of Munich, Germany.
- Regina Kaiser & Agustín Maravall, 1999.
"Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter,"
9912, Banco de España;Working Papers Homepage.
- Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
- Christian J. Murray, 2003. "Cyclical Properties of Baxter-King Filtered Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 472-476, May.
- Timothy Cogley & James M. Nason, 1991. "Effects of the Hodrick-Prescott filter on integrated time series," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
- King, Robert G. & Rebelo, Sergio T., 1993.
"Low frequency filtering and real business cycles,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 17(1-2), pages 207-231.
- Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
- Canova, Fabio, 1993.
"Detrending and Business Cycle Facts,"
CEPR Discussion Papers
782, C.E.P.R. Discussion Papers.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:6574. 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: (Joachim Winter)
If references are entirely missing, you can add them using this form.