Robust exponential smoothing

The paper is devoted to robust modifications of exponential smoothing for time series with outliers or long-tailed distributions. Classical exponential smoothing applied to such time series is sensitive to the presence of outliers or long-tailed distributions and may give inadequate smoothing and forecasting results. First, simple and double exponential smoothing in the L₁ norm (i.e. based on the least absolute deviations) are discussed in detail. Then, general exponential smoothing is made robust, replacing the least squares approach by M-estimation in such a way that the recursive character of the final formulas is preserved. The paper gives simple algorithmic procedures which preserve advantageous features of classical exponential smoothing and, in addition, which are less sensitive to outliers. Robust versions are compared numerically with classical ones.