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Wiener–Kolmogorov Filtering, Frequency-Selective Filtering, And Polynomial Regression

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  • Pollock, D.S.G.

Abstract

Adaptations of the classical Wiener–Kolmogorov filters are described that enable them to be applied to short nonstationary sequences. Alternative filtering methods that operate in the time domain and the frequency domain are described. The frequency-domain methods have the advantage of allowing components of the data to be separated along sharp dividing lines in the frequency domain, without incurring any leakage. The paper contains a novel treatment of the start-up problem that affects the filtering of trended data sequences.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:01:p:71-88_07
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    Citations

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    Cited by:

    1. Stephen Pollock, 2014. "Trends Cycles and Seasons: Econometric Methods of Signal Extraction," Discussion Papers in Economics 14/04, Division of Economics, School of Business, University of Leicester.
    2. Ahmed Belhadjayed & Grégoire Loeper & Frédéric Abergel, 2016. "Forecasting Trends With Asset Prices," Post-Print hal-01512431, HAL.
    3. Macaro, Christian, 2010. "Bayesian non-parametric signal extraction for Gaussian time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 381-395, August.
    4. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    5. D. Stephen G. Pollock, 2018. "Filters, Waves and Spectra," Econometrics, MDPI, vol. 6(3), pages 1-33, July.
    6. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.
    7. D. S. G. Pollock, 2016. "Econometric Filters," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 669-691, December.
    8. D.S.G. Pollock, 2018. "The Manual for IDEOLOG.PAS. A Program for Filtering Econometric Data," Discussion Papers in Economics 19/09, Division of Economics, School of Business, University of Leicester.
    9. D.S.G. Pollock, "undated". "Filters, Waves and Spectra," Discussion Papers in Economics 19/08, Division of Economics, School of Business, University of Leicester.
    10. D.S.G. Pollock, 2009. "IDEOLOG: A Program for Filtering Econometric Data -- A Synopsis of Alternative Methods," EHUCHAPS, in: Ignacio Díaz-Emparanza & Petr Mariel & María Victoria Esteban (ed.), Econometrics with gretl. Proceedings of the gretl Conference 2009, edition 1, chapter 2, pages 15-44, Universidad del País Vasco - Facultad de Ciencias Económicas y Empresariales.

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