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|
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- 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.
- 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.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band Pass Filter,"
NBER Working Papers
7257, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Velasco, Carlos, 1999.
"Non-stationary log-periodogram regression,"
Journal of Econometrics,
Elsevier, vol. 91(2), pages 325-371, August.
- Velasco, 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.
- 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.
- Canova, Fabio, 1993.
"Detrending and Business Cycle Facts,"
CEPR Discussion Papers
782, C.E.P.R. Discussion Papers.
- 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, R.G. & Rebelo, S.T., 1989.
"Low Frequency Filtering And Real Business Cycles,"
RCER Working Papers
205, University of Rochester - Center for Economic Research (RCER).
- 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.
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