Identification of Multiple Outliers in Time Series

  • Thomas Flak
  • Wolfgang Schmid
Conference paper


In order to find outliers in a data set, mostly consecutive procedures are applied. In literature it is distinguished between consecutive inward testing and consecutive outward testing e.g. Barnett/Lewis (1984), Davies/Gather (1992), Using an inward testing procedure it is additionally assumed that an upper bound s for the number of outliers is known.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abraham, B. and Chuang, A. (1989). Outlier detection and time series modeling. Technometrics, 31, p. 241–248.CrossRefGoogle Scholar
  2. Barnett, V. and Lewis, T. (1984), Outliers in Statistical Data. Wiley.Google Scholar
  3. Brockwell, P.J. and Davis, R.A. (1991). Time Series. Springer-Verlag.Google Scholar
  4. Burns, G.C. (1980). Procedures for the detection of outliers in weekly time series. ASAProBuEc, p. 560–563.Google Scholar
  5. Davies, L. and Gather, U. (1992). The identification of multiple outliers. To appear in JASA.Google Scholar
  6. Lee, J.H. and Wei, W.W.S. (1988), A robust procedure for detecting outliers in time series. ASAProBuEc, p. 522–526.Google Scholar
  7. Martin, R.D. and Yohai, V.J. (1985), Robustness in time series and estimating ARMA-models. In: Handbook of Statistics, Vol. 5, Hannan, E.J., Krishnaiah, P.R. and Rao, M.M., eds, Elsevier Science Publishers, p. 119–155.Google Scholar
  8. Schmid, W. (1991), Classification of type I and II outliers. Methods of OR, 64.Google Scholar
  9. Simonoff, J.S. (1991). General approaches to stepwise identification of unusual values in data analysis. In: Directions in Robust Statistics and Diagnostics, Stahel/Weisberg, eds, Springer-Verlag, p. 223–241.Google Scholar
  10. Tiao, G.C. (1985). ARMA models, intervention problems and outlier detection in time series. In: Handbook of Statistics, Vol.5, Hannan, E.J., Krishnaiah, P.R. and Rao, M.M., eds, Elsevier Science Publishers, p. 85–118.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Thomas Flak
    • 1
  • Wolfgang Schmid
    • 1
  1. 1.Abteilung StochastikUniversität UlmUlmGermany

Personalised recommendations