General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series
AbstractA class of model-based filters for extracting trends and cycles in economic time series is presented. These lowpass and bandpass filters are derived in a mutually consistent manner as the joint solution to a signal extraction problem in an unobserved-components model. The resulting trends and cycles are computed in finite samples using the Kalman filter and associated smoother. The filters form a class which is a generalization of the class of Butterworth filters, widely used in engineering. They are very flexible and have the important property of allowing relatively smooth cycles to be extracted from economic time series. Perfectly sharp, or ideal, bandpass filters emerge as a limiting case. Applying the method to quarterly series on U.S. investment and GDP shows a clearly defined cycle. © 2003 President and Fellows of Harvard College and the Massachusetts Institute of Technology.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by MIT Press in its journal Review of Economics and Statistics.
Volume (Year): 85 (2003)
Issue (Month): 2 (May)
Contact details of provider:
Web page: http://mitpress.mit.edu/journals/
Other versions of this item:
- Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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.:
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band Pass Filter,"
NBER Working Papers
7257, National Bureau of Economic Research, Inc.
- Koopman, Siem Jan & Harvey, Andrew, 2003.
"Computing observation weights for signal extraction and filtering,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 27(7), pages 1317-1333, May.
- A. C. Harvey & Siem Jan Koopman, 2000. "Computing Observation Weights for Signal Extraction and Filtering," Econometric Society World Congress 2000 Contributed Papers 0888, Econometric Society.
- Marianne Baxter & Robert G. King, 1995.
"Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series,"
NBER Working Papers
5022, National Bureau of Economic Research, Inc.
- Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
- Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
- 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.
- Ken Matheny & Simon van Norden & Robert Vigfusson, 1989. "GAUSS code for the Hodrick-Prescott filter," QM&RBC Codes 2, Quantitative Macroeconomics & Real Business Cycles, revised Apr 1995.
- Kurt Annen, 2004. "Matlab functions for HP-filter," QM&RBC Codes 166, Quantitative Macroeconomics & Real Business Cycles.
- Edward C. Prescott, 1982. "FORTRAN code for the Hodrick-Prescott filter," QM&RBC Codes 3, Quantitative Macroeconomics & Real Business Cycles.
- Ivailo Izvorski, . "MATLAB code for the Hodrick-Prescott filter," QM&RBC Codes 1, Quantitative Macroeconomics & Real Business Cycles.
- Kurt Annen, 2006. "HP-Filter Excel Add-In," QM&RBC Codes 165, Quantitative Macroeconomics & Real Business Cycles.
- Christian Zimmermann, 2005. "HP-Filter code (Perl)," QM&RBC Codes 98, Quantitative Macroeconomics & Real Business Cycles.
- Kurt Annen, 2006. "HP-Filter DLL executable," QM&RBC Codes 167, Quantitative Macroeconomics & Real Business Cycles.
- Kurt Annen, 2004. "HP-filter for Java," QM&RBC Codes 168, Quantitative Macroeconomics & Real Business Cycles.
- Morten Ravn, . "GAUSS program for Hodrick-Prescott filter," QM&RBC Codes 101, Quantitative Macroeconomics & Real Business Cycles.
- Morten Ravn, . "Alternate GAUSS program for the Hodrick-Prescott Filter," QM&RBC Codes 102, Quantitative Macroeconomics & Real Business Cycles.
- Christian Zimmermann, 2005. "HP-Filter (web interface)," QM&RBC Codes 97, Quantitative Macroeconomics & Real Business Cycles.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Karie Kirkpatrick).
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.