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Biometrika 2000 87(4):789-804; doi:10.1093/biomet/87.4.789
© 2000 by Biometrika Trust
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Outliers in multivariate time series

Ruey S. Tsay, Daniel Peña and Alan E. Pankratz

Graduate School of Business, University of Chicago, Chicago, Illinois 60637, U.S.A. ruey.tsay@gsb.uchicago.edu Department of Statistics and Econometrics, Universidad Carlos III, Cl. Madrid 126, 28903 Getafe, Spain dpena@est-econ.uc3m.es Department of Economics and Management, DePauw University, Greencastle, Indiana 46135, U.S.A.graywolf@depauw.edu

This paper generalises four types of disturbance commonly used in univariate time series analysis to the multivariate case, highlights the differences between univariate and multivariate outliers, and investigates dynamic effects of a multivariate outlier on individual components. The effect of a multivariate outlier depends not only on its size and the underlying model, but also on the interaction between the size and the dynamic structure of the model. The latter factor does not appear in the univariate case. A multivariate outlier can introduce various types of outlier for the marginal component models. By comparing and contrasting results of univariate and multivariate outlier detections, one can gain insights into the characteristics of an outlier. We use real examples to demonstrate the proposed analysis.

Key Words: Additive outlier; Innovational outlier; Level shift; Temporary change.


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