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The Band pass filter

  • Lawrence J. Christiano
  • Terry J. Fitzgerald

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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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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  1. 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.
  2. V.V. Chari & Lawrence J. Christiano & Martin Eichenbaum, 1996. "Expectation traps and discretion," Working Paper Series, Macroeconomic Issues WP-96-5, Federal Reserve Bank of Chicago.
  3. 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.
  4. 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.
  5. Athanasios Orphanides & Simon van Norden, 1999. "The reliability of output gap estimates in real time," Finance and Economics Discussion Series 1999-38, Board of Governors of the Federal Reserve System (U.S.).
  6. 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.
  7. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
  8. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Unit roots in real GNP: do we know, and do we care?," Working Paper Series, Macroeconomic Issues 90-2, Federal Reserve Bank of Chicago.
  9. 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.
  10. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
  11. William Poole, 1999. "Monetary policy rules?," Speech 81, Federal Reserve Bank of St. Louis.
  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.
  13. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
  14. 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.
  15. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  22. 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).
  23. 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.
  24. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678.
  25. 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.
  26. 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.
  27. 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.
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