Reallocation outliers in time series

Wu, L. S.-Y., Ravishanker, N., and Hosking, J. R. M. (1993). Reallocation outliers in time series. Applied Statistics, 42, 301-313.

Abstract. Time series data often contain outliers which have an effect on parameter estimates and forecasts. Outliers occurring 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 behavior 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.

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