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Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering

  • Tucker S. McElroy
  • Thomas M. Trimbur

This paper sets out the theoretical foundations for continuous-time signal extraction in econometrics. Continuous-time modeling gives an effective strategy for treating stock and flow data, irregularly spaced data, and changing frequency of observation. We rigorously derive the optimal continuous-lag filter when the signal component is nonstationary, and provide several illustrations, including a new class of continuous-lag Butterworth filters for trend and cycle estimation.

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File URL: http://www.federalreserve.gov/pubs/feds/2007/200768/200768pap.pdf
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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2007-68.

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Date of creation: 2007
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Handle: RePEc:fip:fedgfe:2007-68
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  1. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Discussion Paper 1997-50, Tilburg University, Center for Economic Research.
  2. Harvey, A. C. & Stock, James H., 1985. "The Estimation of Higher-Order Continuous Time Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 1(01), pages 97-117, April.
  3. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
  4. Thomas M. Trimbur, 2006. "Properties of higher order stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 1-17, 01.
  5. 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.
  6. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(03), pages 365-383, December.
  7. Stock, James H, 1987. "Measuring Business Cycle Time," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1240-61, December.
  8. Chambers, Marcus J. & McGarry, Joanne S., 2002. "Modeling Cyclical Behavior With Differential-Difference Equations In An Unobserved Components Framework," Econometric Theory, Cambridge University Press, vol. 18(02), pages 387-419, April.
  9. Stock, James H., 1987. "Measuring Business Cycle Time," Scholarly Articles 3425950, Harvard University Department of Economics.
  10. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  11. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
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