Reallocation Outliers in Time Series

Lilian Shiao‐Yen Wu, J. R. M. Hosking and Nalini Ravishanker

Journal of the Royal Statistical Society Series C, 1993, vol. 42, issue 2, 301-313

Abstract: Time series data often contain outliers which have an effect on parameter estimates and forecasts. Outliers in isolation have been well studied. However, in business and economic data, it is common to see unusually low observations followed by unusually high observations or vice versa. We model this behaviour by using a new type of multiple time period outlier which we call a reallocation, defined to be a block of unusually high and low values occurring in such a way that the sum of the observations within the block is the same as might have been expected for an undisturbed series. We derive tests for detecting reallocation outliers and distinguishing them from additive outliers. We show the effect on forecasts and forecast intervals of ignoring reallocation outliers. Finally, we apply our methods to two example data sets.

Date: 1993
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