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The Band pass filter

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Author Info
Lawrence J. Christiano
Terry J. Fitzgerald

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Abstract

The "ideal" band-pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies, but applying this filter requires a data set of infinite length. In practice, some sort of approximation is needed. Using projections, the authors derive approximations that are optimal when the time-series representations underlying the raw data have a unit root, or are stationary about a trend.

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File URL: http://www.clevelandfed.org/Research/workpaper/1999/Wp9906.pdf
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Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 9906.

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Length: 1-71
Date of creation: 1999
Date of revision:
Handle: RePEc:fip:fedcwp:9906

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Keywords: Time-series analysis;

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References listed on IDEAS
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  2. James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Lawrence J. Cristiano & Terry J. Fitzgerald, 1998. "The business cycle: it's still a puzzle," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q IV, pages 56-83. [Downloadable!]
  4. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May. [Downloadable!] (restricted)
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  6. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-27, July.
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  7. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February. [Downloadable!] (restricted)
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  8. Ireland, Peter N., 1999. "Does the time-consistency problem explain the behavior of inflation in the United States?," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 279-291, October. [Downloadable!] (restricted)
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  9. 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. [Downloadable!]
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  10. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November. [Downloadable!] (restricted)
  11. Chari, V. V. & Christiano, Lawrence J. & Eichenbaum, Martin, 1998. "Expectation Traps and Discretion," Journal of Economic Theory, Elsevier, vol. 81(2), pages 462-492, August. [Downloadable!] (restricted)
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  12. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August. [Downloadable!] (restricted)
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  13. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-49, September. [Downloadable!] (restricted)
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  15. 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. [Downloadable!] (restricted)
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  16. King, Robert G. & Watson, Mark W., 1994. "The post-war U.S. phillips curve: a revisionist econometric history," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 157-219, December. [Downloadable!] (restricted)
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  17. Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA. [Downloadable!]
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  18. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678. [Downloadable!] (restricted)
  19. Ball, Laurence & Mankiw, N. Gregory, 1994. "A sticky-price manifesto," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 127-151, December. [Downloadable!] (restricted)
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  20. Lawrence J. Christiano & Martin Eichenbaum, 1989. "Unit Roots in Real GNP: Do We Know, and Do We Care?," NBER Working Papers 3130, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  21. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-14, December. [Downloadable!] (restricted)
  22. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August. [Downloadable!] (restricted)
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  23. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71. [Downloadable!]
  24. St-Amant, P. & van Norden, S., 1997. "Measurement of the Output Gap: A Discussion of Recent Research at the Bank of Canada," Technical Reports 79, Bank of Canada. [Downloadable!]
  25. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-91, June. [Downloadable!] (restricted)
  26. William Poole, 1999. "Monetary policy rules?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 3-12. [Downloadable!]
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  27. Singleton, Kenneth J., 1988. "Econometric issues in the analysis of equilibrium business cycle models," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 361-386. [Downloadable!] (restricted)
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