To obtain a robust version of exponential and Holt-Winters smoothing the idea of M-estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast errors on average. The forecast performance is further improved upon by using auxiliary robust starting values and robust scale estimates.
Gelper, S. E. C., Croux, C., & Fried, R. (2008). Computational aspects of robust Holt-Winters smoothing based on M-estimation. Applications of Mathematics, 53(3), 163-176. https://doi.org/10.1007/s10492-008-0002-4