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The Band pass filter

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  • Lawrence J. Christiano
  • Terry J. Fitzgerald

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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Bibliographic Info

Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 9906.

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Date of creation: 1999
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Handle: RePEc:fip:fedcwp:9906

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Keywords: Time-series analysis;

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References

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  1. Lawrence J. Christiano & Martin Eichenbaum, 1989. "Unit roots in real GNP: do we know, and do we care?," Discussion Paper / Institute for Empirical Macroeconomics 18, Federal Reserve Bank of Minneapolis.
  2. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
  3. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678.
  4. Lawrence J. Christiano & Wouter J. Den Haan, 1995. "Small Sample Properties of GMM for Business Cycle Analysis," NBER Technical Working Papers 0177, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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).
  8. 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.
  9. Laurence Ball & N. Gregory Mankiw, 1994. "A sticky-price manifesto," Proceedings, Federal Reserve Bank of Dallas, issue Apr.
  10. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. 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.
  12. V.V. Chari & Lawrence J. Christiano & Martin Eichenbaum, 1996. "Expectations, traps and discretion," Working Papers in Applied Economic Theory 96-04, Federal Reserve Bank of San Francisco.
  13. Robert J. Barro & David B. Gordon, 1981. "A Positive Theory of Monetary Policy in a Natural-Rate Model," NBER Working Papers 0807, National Bureau of Economic Research, Inc.
  14. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
  15. 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.
  16. Cooley, T.F. & Ohanian, L.E., 1989. "The Cyclical Behavior Of Prices," RCER Working Papers 188, University of Rochester - Center for Economic Research (RCER).
  17. Peter N. Ireland, 1998. "Does the Time-Consistency Problem Explain the Behavior of Inflation in the United States?," Boston College Working Papers in Economics 415, Boston College Department of Economics.
  18. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  19. William Poole, 1999. "Monetary policy rules?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 3-12.
  20. 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.
  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.
  22. 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.
  23. 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.
  24. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 9-22.
  25. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
  26. Robert G. King & Mark W. Watson, 1994. "The post-war U.S. Phillips curve: a revisionist econometric history," Working Paper Series, Macroeconomic Issues 94-14, Federal Reserve Bank of Chicago.
  27. 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.
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  1. The long and short of the AIG bailout
    by Scott Condie in econosseur on 2009-01-08 23:19:13
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