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Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules

Author

Listed:
  • Trimbur Thomas

    (Federal Reserve Board – Research and Statistics, 20th and C St, NW 3003 Van Ness Street, NW, Washington, District of Columbia 20008, USA)

  • McElroy Tucker

    (U.S. Census Bureau – CSRM, 4600 Silver Hill Road, D.C., District of Columbia 20233, USA)

Abstract

This paper presents a flexible framework for signal extraction of time series measured as stock or flow at diverse sampling frequencies. Our approach allows for a coherent treatment of series across diverse sampling rules, a deeper understanding of the main properties of signal estimators and the role of measurement, and a straightforward method for signal estimation and interpolation for discrete observations. We set out the essential theoretical foundations, including a proof of the continuous-time Wiener-Kolmogorov formula generalized to nonstationary signal or noise. Based on these results, we derive a new class of low-pass filters that provide the basis for trend estimation of stock and flow time series. Further, we introduce a simple and accurate method for low-frequency signal estimation and interpolation in discrete samples, and examine its properties for simulated series. Illustrations are given on economic data.

Suggested Citation

  • Trimbur Thomas & McElroy Tucker, 2017. "Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-37, January.
    • Handle: RePEc:bpj:jtsmet:v:9:y:2017:i:1:p:37:n:1
    DOI: 10.1515/jtse-2014-0026
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    References listed on IDEAS

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    1. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    2. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    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. Theodore Alexandrov & Silvia Bianconcini & Estela Bee Dagum & Peter Maass & Tucker S. McElroy, 2012. "A Review of Some Modern Approaches to the Problem of Trend Extraction," Econometric Reviews, Taylor & Francis Journals, vol. 31(6), pages 593-624, November.
    5. Tucker McElroy, 2013. "Forecasting continuous-time processes with applications to signal extraction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 439-456, June.
    6. Tucker McElroy & Thomas M. Trimbur, 2011. "On the Discretization of Continuous-Time Filters for Nonstationary Stock and Flow Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 30(5), pages 475-513, October.
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