IDEAS home Printed from https://ideas.repec.org/p/urv/wpaper/2072-261539.html
   My bibliography  Save this paper

On the invertibility of seasonally adjusted series

Author

Listed:
  • Gil-Alana, Luis
  • Lovcha, Yuliya
  • Pérez Laborda, Àlex

Abstract

This paper examines the implications of the seasonal adjustment by an ARIMA model based (AMB) approach in the context of seasonal fractional integration. According to the AMB approach, if the model identified from the data contains seasonal unit roots, the adjusted series will not be invertible that has serious implications for the posterior analysis. We show that even if the ARIMA model identified from the data contains seasonal unit roots, if the true data generating process is stationary seasonally fractionally integrated (as it is often found in economic data), the AMB seasonal adjustment produces dips in the periodogram at seasonal frequencies, but the adjusted series still can be approximated by an invertible process. We also perform a small Monte Carlo study of the log-periodogram regression with tapered data for negative seasonal fractional integration. An empirical application for the Spanish economy that illustrates our results is also carried out at the end of the article. JEL Classification: C15. Keywords: seasonality; invertibility; fractional integration; TRAMO-Seats; tapering

Suggested Citation

  • Gil-Alana, Luis & Lovcha, Yuliya & Pérez Laborda, Àlex, 2016. "On the invertibility of seasonally adjusted series," Working Papers 2072/261539, Universitat Rovira i Virgili, Department of Economics.
    • Handle: RePEc:urv:wpaper:2072/261539
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/2072/261539
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Josu Arteche & Peter M. Robinson, 2000. "Semiparametric Inference in Seasonal and Cyclical Long Memory Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 1-25, January.
    2. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    3. Grether, D M & Nerlove, M, 1970. "Some Properties of 'Optimal' Seasonal Adjustment," Econometrica, Econometric Society, vol. 38(5), pages 682-703, September.
    4. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    5. Víctor Gómez & Agustín Maravall, 1998. "Seasonal Adjustment and Signal Extraction in Economic Time Series," Working Papers 9809, Banco de España.
    6. Ooms, Marius & Hassler, Uwe, 1997. "On the effect of seasonal adjustment on the log-periodogram regression," Economics Letters, Elsevier, vol. 56(2), pages 135-141, October.
    7. Hassler, Uwe & Rodrigues, Paulo M.M. & Rubia, Antonio, 2009. "Testing For General Fractional Integration In The Time Domain," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1793-1828, December.
    8. Edward E. Leamer, 2009. "Macroeconomic Patterns and Stories," Springer Books, Springer, number 978-3-540-46389-4, June.
    9. Arteche, Josu & Robinson, Peter M., 1998. "Seasonal and cyclical long memory," LSE Research Online Documents on Economics 2241, London School of Economics and Political Science, LSE Library.
    10. J. Arteche & C. Velasco, 2005. "Trimming and Tapering Semi‐Parametric Estimates in Asymmetric Long Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 581-611, July.
    11. Bhardwaj, Geetesh & Swanson, Norman R., 2006. "An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 539-578.
    12. Jeremy Berkowitz & Francis X. Diebold, 1998. "Bootstrapping Multivariate Spectra," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 664-666, November.
    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. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    2. Gil-Alaña, Luis A., 2000. "Deterministic seasonality versus seasonal fractional integration," SFB 373 Discussion Papers 2000,106, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    4. Voges, Michelle & Leschinski, Christian & Sibbertsen, Philipp, 2017. "Seasonal long memory in intraday volatility and trading volume of Dow Jones stocks," Hannover Economic Papers (HEP) dp-599, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    5. L.A. Gil-Alana, 2005. "Fractional Cyclical Structures & Business Cycles in the Specification of the US Real Output," European Research Studies Journal, European Research Studies Journal, vol. 0(1-2), pages 99-126.
    6. F. DePenya & L. Gil-Alana, 2006. "Testing of nonstationary cycles in financial time series data," Review of Quantitative Finance and Accounting, Springer, vol. 27(1), pages 47-65, August.
    7. Soares, Lacir Jorge & Souza, Leonardo Rocha, 2006. "Forecasting electricity demand using generalized long memory," International Journal of Forecasting, Elsevier, vol. 22(1), pages 17-28.
    8. Dominique Guegan & Zhiping Lu, 2009. "Wavelet Method for Locally Stationary Seasonal Long Memory Processes," Post-Print halshs-00375531, HAL.
    9. Masaki Narukawa, 2016. "Semiparametric Whittle estimation of a cyclical long-memory time series based on generalised exponential models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 272-295, June.
    10. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    11. L.A. Gil-Alanaa, 2007. "Testing The Existence of Multiple Cycles in Financial and Economic Time Series," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 1-20, May.
    12. Niels Haldrup & Oskar Knapik & Tommaso Proietti, 2016. "A generalized exponential time series regression model for electricity prices," CREATES Research Papers 2016-08, Department of Economics and Business Economics, Aarhus University.
    13. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    14. Luis Gil-Alana, 2010. "A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics," Empirical Economics, Springer, vol. 38(2), pages 471-501, April.
    15. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
    16. García Enríquez, Javier & Arteche González, Jesús María & Murillas Maza, Arantza, 2010. "Fractional Integration Analysis and its Implications on Profitability: the Case of the Mackerel Market in the Basque Country," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    17. Leschinski, Christian & Sibbertsen, Philipp, 2014. "Model Order Selection in Seasonal/Cyclical Long Memory Models," Hannover Economic Papers (HEP) dp-535, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    18. Guglielmo Caporale & Luis Gil-Alana, 2014. "Fractional integration and cointegration in US financial time series data," Empirical Economics, Springer, vol. 47(4), pages 1389-1410, December.
    19. Luis Gil-Alana, 2003. "Strong dependence in the real interest rates," Applied Economics, Taylor & Francis Journals, vol. 35(2), pages 119-124.

    More about this item

    Keywords

    Simulació; Mètodes de; 33 - Economia;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:urv:wpaper:2072/261539. 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: Ariadna Casals (email available below). General contact details of provider: https://edirc.repec.org/data/deurves.html .

    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.