IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v6y2018i3p35-d160445.html
   My bibliography  Save this article

Filters, Waves and Spectra

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/6/3/35/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/6/3/35/
    Download Restriction: no
    ---><---

    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, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. D. S. G. Pollock, 2016. "Econometric Filters," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 669-691, December.
    2. D.S.G. Pollock, "undated". "Filters, Waves and Spectra," Discussion Papers in Economics 19/08, Division of Economics, School of Business, University of Leicester.
    3. Kufenko, Vadim, 2016. "Spurious periodicities in cliometric series: Simultaneous testing," Violette Reihe: Schriftenreihe des Promotionsschwerpunkts "Globalisierung und Beschäftigung" 48/2016, University of Hohenheim, Carl von Ossietzky University Oldenburg, Evangelisches Studienwerk.
    4. Viv B. Hall & Peter Thomson, 2021. "Does Hamilton’s OLS Regression Provide a “better alternative” to the Hodrick-Prescott Filter? A New Zealand Business Cycle Perspective," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 151-183, November.
    5. Baffes, John & Kabundi, Alain, 2023. "Commodity price shocks: Order within chaos?," Resources Policy, Elsevier, vol. 83(C).
    6. Rua, Antonio & Nunes, Luis C., 2005. "Coincident and leading indicators for the euro area: A frequency band approach," International Journal of Forecasting, Elsevier, vol. 21(3), pages 503-523.
    7. Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 75-102, February.
    8. Wolfgang Nierhaus & Timo Wollmershäuser, 2016. "ifo Konjunkturumfragen und Konjunkturanalyse: Band II," ifo Forschungsberichte, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 72, October.
    9. Zivile Zekaite & Gabe de Bondt & Elke Hahn, 2017. "Alice: A New Inflation Monitoring Tool," EcoMod2017 10414, EcoMod.
    10. 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.
    11. Cravo, Túlio A., 2011. "Are small employers more cyclically sensitive? Evidence from Brazil," Journal of Macroeconomics, Elsevier, vol. 33(4), pages 754-769.
    12. de Carvalho, Miguel & Rua, António, 2017. "Real-time nowcasting the US output gap: Singular spectrum analysis at work," International Journal of Forecasting, Elsevier, vol. 33(1), pages 185-198.
    13. Thierry Aimar & Francis Bismans & Claude Diebolt, 2010. "Le cycle économique : une synthèse," Revue Française d'Économie, Programme National Persée, vol. 24(4), pages 3-65.
    14. Ritabrata Bose & Ashima Goyal, 2020. "Disaggregated Indian industrial cycles: A Spectral analysis," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2020-033, Indira Gandhi Institute of Development Research, Mumbai, India.
    15. Luc Dresse & Christophe Van Nieuwenhuyze, 2008. "Do survey indicators let us see the business cycle ? A frequency decomposition," Working Paper Research 131, National Bank of Belgium.
    16. Calcagnini, Giorgio & Travaglini, Giuseppe, 2014. "A time series analysis of labor productivity. Italy versus the European countries and the U.S," Economic Modelling, Elsevier, vol. 36(C), pages 622-628.
    17. Rodríguez, Gabriel, 2010. "Using A Forward-Looking Phillips Curve to Estimate the Output Gap in Peru," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 6(01-2), pages 1-13, April.
    18. Dutra, Tiago Mota & Dias, José Carlos & Teixeira, João C.A., 2022. "Measuring financial cycles: Empirical evidence for Germany, United Kingdom and United States of America," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 599-630.
    19. Saini, Seema & Ahmad, Wasim & Bekiros, Stelios, 2021. "Understanding the credit cycle and business cycle dynamics in India," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 988-1006.
    20. Jasper de Winter & Siem Jan Koopman & Irma Hindrayanto & Anjali Chouhan, 2017. "Modeling the business and financial cycle in a multivariate structural time series model," DNB Working Papers 573, Netherlands Central Bank, Research Department.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jecnmx:v:6:y:2018:i:3:p:35-:d:160445. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.