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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
Handle: RePEc:fip:fedcwp:9906
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  1. 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.
  2. Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA.
  3. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  4. Orphanides, Athanasios, 1999. "The Quest for Prosperity Without Inflation," Working Paper Series 93, Sveriges Riksbank (Central Bank of Sweden).
  5. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64 Elsevier.
  6. 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.
  7. Laurence Ball & N. Gregory Mankiw, 1994. "A Sticky-Price Manifesto," NBER Working Papers 4677, National Bureau of Economic Research, Inc.
  8. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Staff Report 102, Federal Reserve Bank of Minneapolis.
  9. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678-678.
  10. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
  11. 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.
  12. 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).
  13. 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.
  14. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, Enero.
  15. Lawrence J. Christiano & Wouter Den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Staff Report 199, Federal Reserve Bank of Minneapolis.
  16. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-749, September.
  17. 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.
  18. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-1014, December.
  19. 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 473-491, June.
  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. Lawrence J. Christiano & 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
  27. William Poole, 1999. "Monetary policy rules?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 3-12.
  28. 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.
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