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Outlier detection in ARMA models

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  • Hamid Louni

Abstract

. We consider an autoregressive moving‐average (ARMA) time series where the observations are perturbed by two kinds of outliers: an additive outlier (AO) or an innovation outlier (IO). Abraham and Yatawara [Journal of Time Series Analysis (1988) Vol. 9, pp. 109–19] investigate a sequential test which successively detects and identifies the outlier type. In this article, we propose an extension of this test, called ‘modified sequential test’, which performs the two procedures simultaneously and coherently. The asymptotic distribution of the test statistic is calculated under the null hypothesis that no outlier is present. Comparison of the two test procedures using simulation experiments shows that the proposed test gives a better power especially in the case of an IO.

Suggested Citation

  • Hamid Louni, 2008. "Outlier detection in ARMA models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1057-1065, November.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:6:p:1057-1065
    DOI: 10.1111/j.1467-9892.2008.00595.x
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    References listed on IDEAS

    as
    1. Francesco Battaglia & Lia Orfei, 2005. "Outlier Detection And Estimation In NonLinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 107-121, January.
    2. Bovas Abraham & Alice Chuang, 1993. "Expectation‐Maximization Algorithms And The Estimation Of Time Series Models In The Presence Of Outliers," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 221-234, May.
    3. Pena, Daniel, 1990. "Influential Observations in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 235-241, April.
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