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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

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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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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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Keywords: Time-series analysis ; Econometrics;

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References listed on IDEAS
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  1. Ravn, Morten O. & Uhlig, Harald, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CEPR Discussion Papers 2858, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Stock, James H, 1987. "Measuring Business Cycle Time," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1240-61, December. [Downloadable!] (restricted)
  3. Thomas M. Trimbur, 2006. "Properties of higher order stochastic cycles," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(1), pages 1-17, 01. [Downloadable!] (restricted)
  4. 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.
    Other versions:
  5. 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. [Downloadable!]
  6. 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, 03. [Downloadable!] (restricted)
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  7. 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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