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Filters, Waves and Spectra

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  • D. Stephen G. Pollock

    (Department of Economics, University of Leciceter, Leicester LE1 7RH, UK)

Abstract

Econometric analysis requires filtering techniques that are adapted to cater to data sequences that are short and that have strong trends. Whereas the economists have tended to conduct their analyses in the time domain, the engineers have emphasised the frequency domain. This paper places its emphasis in the frequency domain; and it shows how the frequency-domain methods can be adapted to cater to short trended sequences. Working in the frequency domain allows an unrestricted choice to be made of the frequency response of a filter. It also requires that the data should be free of trends. Methods for extracting the trends prior to filtering and for restoring them thereafter are described.

Suggested Citation

  • D. Stephen G. Pollock, 2018. "Filters, Waves and Spectra," Econometrics, MDPI, vol. 6(3), pages 1-33, July.
    • Handle: RePEc:gam:jecnmx:v:6:y:2018:i:3:p:35-:d:160445
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    References listed on IDEAS

    as
    1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    2. Pollock D. S. G., 2013. "Cycles, Syllogisms and Semantics: Examining the Idea of Spurious Cycles," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 81-102, September.
    3. 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.
    4. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Division of Economics, School of Business, University of Leicester.
    5. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1.
    6. Wallis, Kenneth F., 1981. "Models For X-11 And 'X-11-Forecast' Procedures For Preliminary And Revised Seasonal Adjustments," Economic Research Papers 269150, University of Warwick - Department of Economics.
    7. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.
    8. 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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    Cited by:

    1. Zhengyuan Gao & Christian M. Hafner, 2019. "Looking Backward and Looking Forward," Econometrics, MDPI, vol. 7(2), pages 1-24, June.
    2. D. Stephen G. Pollock, 2020. "Linear Stochastic Models in Discrete and Continuous Time," Econometrics, MDPI, vol. 8(3), pages 1-22, September.
    3. D. Stephen G. Pollock, 2021. "Enhanced Methods of Seasonal Adjustment," Econometrics, MDPI, vol. 9(1), pages 1-23, January.

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