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.
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- 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.
- Canova, Fabio, 1998.
"Detrending and business cycle facts,"
Journal of Monetary Economics,
Elsevier, vol. 41(3), pages 475-512, May.
- Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
- 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.
- Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- João Valle e Azevedo, 2007. "Exact Limit of the Expected Periodogram in the Unit-Root case," Working Papers 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," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
- Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Working Papers 9912, Banco de España;Working Papers Homepage.
- 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 231-247, July-Sept.
- 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, "undated". "CFFILTER: RATS procedure to perform band pass filter using Christiano-Fitzgerald method," Statistical Software Components RTS00034, Boston College Department of Economics.
- Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
- Velasco Gómez, Carlos, 1998. "Non-stationary log-periodogram regression," DES - Working Papers. Statistics and Econometrics. WS 4554, Universidad Carlos III de Madrid. Departamento de Estadística.
- 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.
- 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.
- 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 365-373, July.
- 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.
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