Computational aspects of robust Holt-Winters smoothing based on M-estimation

Article

Abstract

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.

Keywords

Holt-Winters smoothing robust methods time series 

References

  1. [1]
    C. Chatfield, A. Koehler, J. Ord, R. Snyder: A new look at models for exponential smoothing. The Statistician 50 (2001), 147–159.MathSciNetGoogle Scholar
  2. [2]
    T. Cipra: Robust exponential smoothing. J. Forecast. 11 (1992), 57–69.CrossRefGoogle Scholar
  3. [3]
    T. Cipra, R. Romera: Kalman filter with outliers and missing observations. Test 6 (1997), 379–395.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Davies, R. Fried, U. Gather: Robust signal extraction for on-line monitoring data. J. Stat. Plann. Inference 122 (2004), 65–78.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    R. Fried: Robust filtering of time series with trends. J. Nonparametric Stat. 16 (2004), 313–328.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    U. Gather, K. Schettlinger, R. Fried: Online signal extraction by robust linear regression. Comput. Stat. 21 (2006), 33–51.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    S. Gelper, R. Fried, C. Croux: Robust forecasting with exponential and Holt-Winters smoothing. Preprint. 2007.Google Scholar
  8. [8]
    C. Holt: Forecasting seasonals and trends by exponentially weighted moving averages. ONR Research Memorandum 52. 1959.Google Scholar
  9. [9]
    A. Kotsialos, M. Papageorgiou, A. Poulimenos: Long-term sales forecasting using Holt-Winters and neural network methods. J. Forecast. 24 (2005), 353–368.CrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Romera, T. Cipra: On practical implementation of robust Kalman filtering. Comm. Stat., Simulation Comput. 24 (1995), 461–488.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    A. Siegel: Robust regression using repeated medians. Biometrika 69 (1982), 242–244.MATHCrossRefGoogle Scholar
  12. [12]
    J. Taylor: Forecasting daily supermarket sales using exponentially weighted quantile regression. Eur. J. Oper. Res. 178 (2007), 154–167.MATHCrossRefGoogle Scholar
  13. [13]
    P. Winters: Forecasting sales by exponentially weighted moving averages. Manage. Sci. 6 (1960), 324–342.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    V. Yohai, R. Zamar: High breakdown-point estimates of regression by means of the minimization of an efficient scale. J. Am. Stat. Assoc. 83 (1988), 406–413.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Fac. of Economics and BusinessK.U. LeuvenLeuvenBelgium
  2. 2.Department of StatisticsUniversity of DortmundDortmundGermany

Personalised recommendations