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The Band pass filter

Listed author(s):
  • 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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  3. 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.
  4. 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.
  5. 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.
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  8. Orphanides, Athanasios, 1999. "The Quest for Prosperity Without Inflation," Working Paper Series 93, Sveriges Riksbank (Central Bank of Sweden).
  9. V. V. Chari & Lawrence J. Christiano & Martin Eichenbaum, 1996. "Expectation Traps and Discretion," NBER Working Papers 5541, National Bureau of Economic Research, Inc.
  10. 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.
  11. 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.
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  20. William Poole, 1999. "Monetary policy rules?," Speech 81, Federal Reserve Bank of St. Louis.
  21. 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.
  22. 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.
  23. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678-678.
  24. 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.
  25. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  26. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
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  28. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
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