# Article

Full entry | PDF   (0.3 MB)
Keywords:
Holt-Winters smoothing; robust methods; time series
Summary:
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. {\it 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.
References:
[1] Chatfield, C., Koehler, A., Ord, J., Snyder, R.: A new look at models for exponential smoothing. The Statistician 50 (2001), 147-159. MR 1831380
[2] Cipra, T.: Robust exponential smoothing. J. Forecast. 11 (1992), 57-69. DOI 10.1002/for.3980110106
[3] Cipra, T., Romera, R.: Kalman filter with outliers and missing observations. Test 6 (1997), 379-395. DOI 10.1007/BF02564705 | MR 1616912 | Zbl 0893.62094
[4] Davies, P., Fried, R., Gather, U.: Robust signal extraction for on-line monitoring data. J. Stat. Plann. Inference 122 (2004), 65-78. DOI 10.1016/j.jspi.2003.06.012 | MR 2057914 | Zbl 1040.62099
[5] Fried, R.: Robust filtering of time series with trends. J. Nonparametric Stat. 16 (2004), 313-328. DOI 10.1080/10485250410001656444 | MR 2073028 | Zbl 1065.62162
[6] Gather, U., Schettlinger, K., Fried, R.: Online signal extraction by robust linear regression. Comput. Stat. 21 (2006), 33-51. DOI 10.1007/s00180-006-0249-8 | MR 2252439 | Zbl 1114.62047
[7] Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt-Winters smoothing. Preprint (2007). MR 2752114
[8] Holt, C.: Forecasting seasonals and trends by exponentially weighted moving averages. ONR Research Memorandum 52 (1959).
[9] Kotsialos, A., Papageorgiou, M., Poulimenos, A.: Long-term sales forecasting using Holt-Winters and neural network methods. J. Forecast. 24 (2005), 353-368. DOI 10.1002/for.943 | MR 2190371
[10] Romera, R., Cipra, T.: On practical implementation of robust Kalman filtering. Comm. Stat., Simulation Comput. 24 (1995), 461-488. DOI 10.1080/03610919508813252 | MR 1333047 | Zbl 0850.62688
[11] Siegel, A.: Robust regression using repeated medians. Biometrika 69 (1982), 242-244. DOI 10.1093/biomet/69.1.242 | Zbl 0483.62026
[12] Taylor, J.: Forecasting daily supermarket sales using exponentially weighted quantile regression. Eur. J. Oper. Res. 178 (2007), 154-167. DOI 10.1016/j.ejor.2006.02.006 | Zbl 1102.62103
[13] Winters, P.: Forecasting sales by exponentially weighted moving averages. Manage. Sci. 6 (1960), 324-342. DOI 10.1287/mnsc.6.3.324 | MR 0112740 | Zbl 0995.90562
[14] Yohai, V., Zamar, R.: High breakdown-point estimates of regression by means of the minimization of an efficient scale. J. Am. Stat. Assoc. 83 (1988), 406-413. DOI 10.1080/01621459.1988.10478611 | MR 0971366 | Zbl 0648.62036

Partner of