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Additive Outlier Detection Via Extreme‐Value Theory

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  • Peter Burridge
  • A. M. Robert Taylor

Abstract

. This article is concerned with detecting additive outliers using extreme value methods. The test recently proposed for use with possibly non‐stationary time series by Perron and Rodriguez [Journal of Time Series Analysis (2003) vol. 24, pp. 193–220], is, as they point out, extremely sensitive to departures from their assumption of Gaussianity, even asymptotically. As an alternative, we investigate the robustness to distributional form of a test based on weighted spacings of the sample order statistics. Difficulties arising from uncertainty about the number of potential outliers are discussed, and a simple algorithm requiring minimal distributional assumptions is proposed and its performance evaluated. The new algorithm has dramatically lower level‐inflation in face of departures from Gaussianity than the Perron–Rodriguez test, yet retains good power in the presence of outliers.

Suggested Citation

  • Peter Burridge & A. M. Robert Taylor, 2006. "Additive Outlier Detection Via Extreme‐Value Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 685-701, September.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:5:p:685-701
    DOI: 10.1111/j.1467-9892.2006.00483.x
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    Cited by:

    1. Olivier Darné & Amélie Charles, 2012. "A note on the uncertain trend in US real GNP: Evidence from robust unit root tests," Economics Bulletin, AccessEcon, vol. 32(3), pages 2399-2406.
    2. Priyanga Dilini Talagala & Rob J Hyndman & Kate Smith-Miles, 2019. "Anomaly Detection in High Dimensional Data," Monash Econometrics and Business Statistics Working Papers 20/19, Monash University, Department of Econometrics and Business Statistics.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Josep Lluís Carrion-I-Silvestre & María Dolores Gadea, 2016. "Bounds, Breaks and Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 165-181, March.
    5. Gabriel Rodriguez & Dionisio Ramirez, 2014. "A Note on the Size of the ADF Test with Additive Outliers and Fractional Errors. A Reappraisal about the (Non)Stationarity of the Latin-American Inflation Series," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, vol. 37(73), pages 113-132.
    6. Priyanga Dilini Talagala & Rob J Hyndman & Catherine Leigh & Kerrie Mengersen & Kate Smith-Miles, 2019. "A Feature-Based Framework for Detecting Technical Outliers in Water-Quality Data from In Situ Sensors," Monash Econometrics and Business Statistics Working Papers 1/19, Monash University, Department of Econometrics and Business Statistics.
    7. Sevvandi Kandanaarachchi & Rob J Hyndman, 2021. "Leave-one-out Kernel Density Estimates for Outlier Detection," Monash Econometrics and Business Statistics Working Papers 2/21, Monash University, Department of Econometrics and Business Statistics.
    8. Sam Astill & David I. Harvey & A. M. Robert Taylor, 2013. "A bootstrap test for additive outliers in non-stationary time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 454-465, July.
    9. Gabriel Rodriguez & Dionisio Ramirez, 2013. "A comparison between Tau-d and the procedure TRAMO-SEATS is also included," Documentos de Trabajo / Working Papers 2013-355, Departamento de Economía - Pontificia Universidad Católica del Perú.
    10. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
    11. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, vol. 3(1), pages 1-31, March.
    12. Alanya-Beltran, Willy, 2022. "Unit roots in lower-bounded series with outliers," Economic Modelling, Elsevier, vol. 115(C).
    13. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2009. "Robust methods for detecting multiple level breaks in autocorrelated time series [Revised to become No. 10/01 above]," Discussion Papers 09/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    14. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2016. "Empirical Likelihood for Outlier Detection and Estimation in Autoregressive Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 315-336, May.
    15. Priyanga Dilini Talagala & Rob J Hyndman & Kate Smith-Miles & Sevvandi Kandanaarachchi & Mario A Munoz, 2018. "Anomaly detection in streaming nonstationary temporal data," Monash Econometrics and Business Statistics Working Papers 4/18, Monash University, Department of Econometrics and Business Statistics.
    16. Chini, Emilio Zanetti, 2023. "Can we estimate macroforecasters’ mis-behavior?," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    17. Chen, Yi-Hsuan & Tu, Anthony H., 2013. "Estimating hedged portfolio value-at-risk using the conditional copula: An illustration of model risk," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 514-528.

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