IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v33y2017i1p1-14n1.html
   My bibliography  Save this article

Unit Root Properties of Seasonal Adjustment and Related Filters: Special Cases

Author

Listed:
  • Bell William.R.

    (U.S. Census Bureau, Washington, DC 20233, United States of America)

Abstract

Bell (2012) catalogued unit root factors contained in linear filters used in seasonal adjustment (model-based or from the X-11 method) but noted that, for model-based seasonal adjustment, special cases could arise where filters could contain more unit root factors than was indicated by the general results. This article reviews some special cases that occur with canonical ARIMA model based adjustment in which, with some commonly used ARIMA models, the symmetric seasonal filters contain two extra nonseasonal differences (i.e., they include an extra (1 - B)(1 - F)). This increases by two the degree of polynomials in time that are annihilated by the seasonal filter and reproduced by the seasonal adjustment filter. Other results for canonical ARIMA adjustment that are reported in Bell (2012), including properties of the trend and irregular filters, and properties of the asymmetric and finite filters, are unaltered in these special cases. Special cases for seasonal adjustment with structural ARIMA component models are also briefly discussed.

Suggested Citation

  • Bell William.R., 2017. "Unit Root Properties of Seasonal Adjustment and Related Filters: Special Cases," Journal of Official Statistics, Sciendo, vol. 33(1), pages 1-14, March.
    • Handle: RePEc:vrs:offsta:v:33:y:2017:i:1:p:1-14:n:1
    DOI: 10.1515/jos-2017-0001
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jos-2017-0001
    Download Restriction: no
    File URL: https://libkey.io/10.1515/jos-2017-0001?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
    ---><---

    References listed on IDEAS

    as
    1. Harvey,Andrew & Koopman,Siem Jan & Shephard,Neil (ed.), 2004. "State Space and Unobserved Component Models," Cambridge Books, Cambridge University Press, number 9780521835954.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    3. Victor Gómez & Agustín Maravall, 1996. "Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996)," Working Papers 9628, Banco de España.
    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. Marczak, Martyna & Proietti, Tommaso, 2016. "Outlier detection in structural time series models: The indicator saturation approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 180-202.
    2. Alexander Tsyplakov, 2011. "An introduction to state space modeling (in Russian)," Quantile, Quantile, issue 9, pages 1-24, July.
    3. 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.
    4. Olivier Darné & Amélie Charles, 2011. "Large shocks in U.S. macroeconomic time series: 1860-1988," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 5(1), pages 79-100, January.
    5. Rodríguez, Alejandro & Ruiz, Esther, 2012. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 62-74, January.
    6. António Alberto Santos, 2010. "MCMC, likelihood estimation and identifiability problems in DLM models," GEMF Working Papers 2010-12, GEMF, Faculty of Economics, University of Coimbra.
    7. Yu, Wei-Choun & Zivot, Eric, 2011. "Forecasting the term structures of Treasury and corporate yields using dynamic Nelson-Siegel models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 579-591.
    8. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    9. Giovanni Angelini & Giuseppe Cavaliere & Luca Fanelli, 2022. "Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 3-22, January.
    10. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    11. David T. Frazier & Ruben Loaiza-Maya & Gael M. Martin, 2021. "Variational Bayes in State Space Models: Inferential and Predictive Accuracy," Papers 2106.12262, arXiv.org, revised Feb 2022.
    12. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    13. Irma Hindrayanto & John A.D. Aston & Siem Jan Koopman & Marius Ooms, 2013. "Modelling trigonometric seasonal components for monthly economic time series," Applied Economics, Taylor & Francis Journals, vol. 45(21), pages 3024-3034, July.
    14. Olivier Darné & Amélie Charles, 2008. "The impact of outliers on transitory and permanent components in macroeconomic time series," Economics Bulletin, AccessEcon, vol. 3(60), pages 1-9.
    15. Theodosiou, Marina, 2011. "Forecasting monthly and quarterly time series using STL decomposition," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1178-1195, October.
    16. repec:jss:jstsof:41:i07 is not listed on IDEAS
    17. Proietti, Tommaso, 2005. "New algorithms for dating the business cycle," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 477-498, April.
    18. Michael Artis & Massimiliano Marcellino & Tommaso Proietti, 2004. "Characterising the Business Cycle for Accession Countries," Working Papers 261, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    19. Fei Gu & Kristopher J. Preacher & Emilio Ferrer, 2014. "A State Space Modeling Approach to Mediation Analysis," Journal of Educational and Behavioral Statistics, , vol. 39(2), pages 117-143, April.
    20. 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.
    21. repec:ebl:ecbull:v:3:y:2008:i:60:p:1-9 is not listed on IDEAS
    22. Bógalo, Juan & Llada, Martín & Poncela, Pilar & Senra, Eva, 2022. "Seasonality in COVID-19 times," Economics Letters, Elsevier, vol. 211(C).

    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:vrs:offsta:v:33:y:2017:i:1:p:1-14: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.sciendo.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.