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On the invertibility of seasonally adjusted series

Author

Listed:
  • Yuliya Lovcha

    () (Universitat Rovira-i-Virgili)

  • Alejandro Perez-Laborda

    (Universitat Rovira-i-Virgili)

  • Luis Gil-Alana

    (Universidad de Navarra)

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.

Suggested Citation

  • Yuliya Lovcha & Alejandro Perez-Laborda & Luis Gil-Alana, 2018. "On the invertibility of seasonally adjusted series," Computational Statistics, Springer, vol. 33(1), pages 443-465, March.
  • Handle: RePEc:spr:compst:v:33:y:2018:i:1:d:10.1007_s00180-017-0715-5
    DOI: 10.1007/s00180-017-0715-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Grether, D M & Nerlove, M, 1970. "Some Properties of 'Optimal' Seasonal Adjustment," Econometrica, Econometric Society, vol. 38(5), pages 682-703, September.
    6. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    7. 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.
    8. Víctor Gómez & Agustín Maravall, 1998. "Seasonal Adjustment and Signal Extraction in Economic Time Series," Working Papers 9809, Banco de España;Working Papers Homepage.
    9. Jeremy Berkowitz & Francis X. Diebold, 1998. "Bootstrapping Multivariate Spectra," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 664-666, November.
    10. 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.
    11. Gil-Alaña, L. A. & Robinson, Peter M., 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," LSE Research Online Documents on Economics 298, London School of Economics and Political Science, LSE Library.
    12. 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.
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    Keywords

    Seasonality; Invertibility; Fractional integration; TRAMO-seats; Tapering;

    JEL classification:

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

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