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

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  • Tucker S. McElroy
  • Thomas M. Trimbur

Abstract

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/2007/200768/200768abs.html
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Bibliographic Info

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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Related research

Keywords: Time-series analysis ; Econometrics;

This paper has been announced in the following NEP Reports:

References

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  1. Stock, James H., 1987. "Measuring Business Cycle Time," Scholarly Articles 3425950, Harvard University Department of Economics.
  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. 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.
  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. Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge.
  6. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Banco de Espa�a Working Papers 0108, Banco de Espa�a.
  7. 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.
  8. 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.
  9. Bergstrom, A. R., 1988. "The History of Continuous-Time Econometric Models," Econometric Theory, Cambridge University Press, vol. 4(03), pages 365-383, December.
  10. Andrew Harvey, 2004. "Trend estimation, signal-noise ratios and the frequency of observations," Econometric Society 2004 Australasian Meetings 343, Econometric Society.
  11. Stock, James H, 1987. "Measuring Business Cycle Time," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1240-61, December.
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Cited by:
  1. Tucker McElroy, 2013. "Forecasting continuous-time processes with applications to signal extraction," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(3), pages 439-456, June.

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