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Detection and estimation of additive outliers in seasonal time series

Author

Listed:
  • Francesco Battaglia

    (University La Sapienza)

  • Domenico Cucina

    (University of Salerno)

  • Manuel Rizzo

    (University La Sapienza)

Abstract

The detection of outliers in a time series is an important issue because their presence may have serious negative effects on the analysis in many different ways. Moreover the presence of a complex seasonal pattern in the series could affect the properties of the usual outlier detection procedures. Therefore modelling the appropriate form of seasonality is a very important step when outliers are present in a seasonal time series. In this paper we present some procedures for detection and estimation of additive outliers when parametric seasonal models, in particular periodic autoregressive, are specified to fit the data. A simulation study is presented to evaluate the benefits and the drawbacks of the proposed procedure on a selection of seasonal time series. An application to three real time series is also examined.

Suggested Citation

  • Francesco Battaglia & Domenico Cucina & Manuel Rizzo, 2020. "Detection and estimation of additive outliers in seasonal time series," Computational Statistics, Springer, vol. 35(3), pages 1393-1409, September.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:3:d:10.1007_s00180-019-00928-5
    DOI: 10.1007/s00180-019-00928-5
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    References listed on IDEAS

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    1. Q. Shao, 2008. "Robust Estimation For Periodic Autoregressive Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 251-263, March.
    2. E. Ursu & Jean-Christophe Pereau, 2014. "Robust modelling of periodic vector autoregressive time series," Post-Print hal-01135627, HAL.
    3. E. Ursu & Jean-Christophe Pereau, 2014. "Robust modelling of periodic vector autoregressive time series," Post-Print hal-01135627, HAL.
    4. Eugen Ursu & Kamil Feridun Turkman, 2012. "Periodic autoregressive model identification using genetic algorithms," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 398-405, May.
    5. Alexander Vosseler & Enzo Weber, 2018. "Forecasting seasonal time series data: a Bayesian model averaging approach," Computational Statistics, Springer, vol. 33(4), pages 1733-1765, December.
    6. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    7. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
    8. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    9. Eugen Ursu & Pierre Duchesne, 2009. "On modelling and diagnostic checking of vector periodic autoregressive time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 70-96, January.
    10. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    11. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521562607.
    12. Baragona, Roberto & Battaglia, Francesco & Calzini, Claudio, 2001. "Genetic algorithms for the identification of additive and innovation outliers in time series," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 1-12, July.
    13. Domenico Cucina & Manuel Rizzo & Eugen Ursu, 2019. "Multiple changepoint detection for periodic autoregressive models with an application to river flow analysis," Post-Print hal-02878506, HAL.
    14. A. I. McLeod, 1994. "Diagnostic Checking Of Periodic Autoregression Models With Application," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 221-233, March.
    15. Sarnaglia, A.J.Q. & Reisen, V.A. & Lévy-Leduc, C., 2010. "Robust estimation of periodic autoregressive processes in the presence of additive outliers," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2168-2183, October.
    16. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
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