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Trends Cycles And Seasons: Econometric Methods Of Signal Extraction

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  • D.S.G. Pollock

Abstract

Alternative methods of trend extraction and of seasonal adjustment are described that operate in the time domain and in the frequency domain. The time-domain methods that are implemented in the TRAMO–SEATS and the STAMP programs are compared. An abbreviated time-domain method of seasonal adjustment that is implemented in the IDEOLOG program is also presented. Finite-sample versions of the Wiener–Kolmogorov filter are described that can be used to implement the methods in a common way. The frequency-domain method, which is also implemented in the IDEOLOG program, employs an ideal frequency selective filter that depends on identifying the ordinates of the Fourier transform of a detrended data sequence that should lie in the pass band of the filter and those that should lie in its stop band. Filters of this nature can be used both for extracting a low-frequency cyclical component of the data and for extracting the seasonal component.

Suggested Citation

  • D.S.G. Pollock, 2017. "Trends Cycles And Seasons: Econometric Methods Of Signal Extraction," Discussion Papers in Economics 17/02, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:17/02
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    References listed on IDEAS

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    1. Maravall, Agustin, 1985. "On Structural Time Series Models and the Characterization of Components," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 350-355, October.
    2. McElroy, Tucker & Sutcliffe, Andrew, 2006. "An iterated parametric approach to nonstationary signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2206-2231, May.
    3. D. S. G. Pollock, 2002. "A review of TSW: the Windows version of the TRAMO-SEATS program," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(3), pages 291-299.
    4. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    5. Pollock, D.S.G., 2007. "Wiener–Kolmogorov Filtering, Frequency-Selective Filtering, And Polynomial Regression," Econometric Theory, Cambridge University Press, vol. 23(1), pages 71-88, February.
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    More about this item

    Keywords

    Time series; Spectral analysis; Business cycles; Turning points; Seasonality.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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