Kybernetika 47 no. 2, 165-178, 2011

Exponential smoothing for time series with outliers

Tomáš Hanzák and Tomáš Cipra


Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data.


exponential smoothing, Kalman filter, outliers, robust smoothing and forecasting


62M10, 62M20, 90A20, 60G35


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