IDEAS home Printed from https://ideas.repec.org/a/bpj/jtsmet/v9y2017i1p37n1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jtse-2014-0026
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/jtse-2014-0026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Thornton, Michael A., 2013. "Removing seasonality under a changing regime: Filtering new car sales," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 4-14.
    2. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    3. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    4. Buono, Dario & Alpay, Kocak, 2010. "Backward recalculation of seasonal series affected by economic crisis: a Model-Based-Link method for the case of Turkish GDP," MPRA Paper 40092, University Library of Munich, Germany.
    5. Barnett, William A. & de Peretti, Philippe, 2009. "Admissible Clustering Of Aggregator Components: A Necessary And Sufficient Stochastic Seminonparametric Test For Weak Separability," Macroeconomic Dynamics, Cambridge University Press, vol. 13(S2), pages 317-334, September.
    6. Wildi, Marc & McElroy, Tucker S., 2019. "The trilemma between accuracy, timeliness and smoothness in real-time signal extraction," International Journal of Forecasting, Elsevier, vol. 35(3), pages 1072-1084.
    7. Dagum, Estela Bee, 2010. "Business Cycles and Current Economic Analysis/Los ciclos económicos y el análisis económico actual," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 577-594, Diciembre.
    8. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    9. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    10. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
    11. Diego Bodas & Juan Ramon Garcia & Juan Murillo & Matias Pacce & Tomasa Rodrigo & Juan de Dios Romero & Pep Ruiz & Camilo Ulloa & Heribert Valero, 2018. "Measuring Retail Trade Using Card Transactional Data," Working Papers 18/03, BBVA Bank, Economic Research Department.
    12. Barend Abeln & Jan P. A. M. Jacobs, 2023. "CAMPLET: Seasonal Adjustment Without Revisions," SpringerBriefs in Economics, in: Seasonal Adjustment Without Revisions, chapter 0, pages 7-29, Springer.
    13. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
    14. Edward E. Leamer, 2011. "Workday, Holiday and Calendar Adjustment with 21st Century Data: Monthly Aggregates from Daily Diesel Fuel Purchases," NBER Working Papers 16897, National Bureau of Economic Research, Inc.
    15. Ghysels, E., 1993. "A Time Series Model with Periodic Stochastic Regime Switching," Cahiers de recherche 9314, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    16. Kubota, Keiichi & Tokunaga, Toshifumi & Wada, Kenji, 2008. "Consumption behavior, asset returns, and risk aversion: Evidence from the Japanese household survey," Japan and the World Economy, Elsevier, vol. 20(1), pages 1-18, January.
    17. Schneider, Nicolas & Strielkowski, Wadim, 2023. "Modelling the unit root properties of electricity data—A general note on time-domain applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    18. Marlon Fritz, 2019. "Data-Driven Local Polynomial Trend Estimation for Economic Data - Steady State Adjusting Trends," Working Papers Dissertations 49, Paderborn University, Faculty of Business Administration and Economics.
    19. Thury, Gerhard & Witt, Stephen F., 1998. "Forecasting industrial production using structural time series models," Omega, Elsevier, vol. 26(6), pages 751-767, December.
    20. Abdur Chowdhury, 1995. "The demand for money in a small open economy: The case of Switzerland," Open Economies Review, Springer, vol. 6(2), pages 131-144, April.

    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:bpj:jtsmet:v:9:y:2017:i:1:p:37:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.