Previous |  Up |  Next


exponential smoothing; Holt--Winters method; irregular time series; seasonal indices; trigonometric functions
The paper suggests a generalization of widely used Holt-Winters smoothing and forecasting method for seasonal time series. The general concept of seasonality modeling is introduced both for the additive and multiplicative case. Several special cases are discussed, including a linear interpolation of seasonal indices and a usage of trigonometric functions. Both methods are fully applicable for time series with irregularly observed data (just the special case of missing observations was covered up to now). Moreover, they sometimes outperform the classical Holt-Winters method even for regular time series. A simulation study and real data examples compare the suggested methods with the classical one.
[1] M. Aldrin, E. Damsleth: Forecasting non-seasonal time series with missing observations. J. Forecasting 8 (1989), 97-116. DOI 10.1002/for.3980080204
[2] C. Chatfield, M. Yar: Holt-Winters forecasting: some practical issues. The Statistician 37 (1988), 129-140. DOI 10.2307/2348687
[3] T. Cipra, T. Hanzák: Exponential smoothing for irregular time series. Kybernetika 44 (2008), 385-399. MR 2436039 | Zbl 1154.62363
[4] T. Cipra, J. Trujillo, A. Rubio: Holt-Winters method with missing observations. Management Sci. 41 (1995), 174-178. DOI 10.1287/mnsc.41.1.174 | Zbl 0829.90034
[5] E. S. Gardner: Exponential smoothing: The state of the art. J. Forecasting 4 (1985), 1-28. DOI 10.1002/for.3980040103
[6] E. S. Gardner: Exponential smoothing: The state of the art - Part II. Internat. J. Forecasting 22 (2006), 637-666. DOI 10.1016/j.ijforecast.2006.03.005
[7] T. Hanzák: Improved Holt method for irregular time series. In: WDS'08 Proc. Contributed Papers, Part I - Mathematics and Computer Sciences, Matfyzpress, Prague 2008, pp. 62-67.
[8] C. C. Holt: Forecasting seasonals and trends by exponentially weighted moving averages. Internat. J. Forecasting 20 (2004), 5-10. DOI 10.1016/j.ijforecast.2003.09.015
[9] R. J. Hyndman: Time Series Data Library, Accessed on 26 June 2010.
[10] R. J. Hyndman, A. B. Koehler, R. D. Snyder, S. Grose: A state space framework for automatic forecasting using exponential smoothing methods. Internat. J. Forecasting 18 (2002), 439-454. DOI 10.1016/S0169-2070(01)00110-8
[11] T. Ratinger: Seasonal time series with missing observations. Appl. Math. 41 (1996), 41-55. MR 1365138 | Zbl 0888.62097
[12] J. W. Taylor: Short-term electricity demand forecasting using double seasonal exponential smoothing. J. Oper. Res. Soc. 54 (2003), 799-805. DOI 10.1057/palgrave.jors.2601589 | Zbl 1097.91541
[13] J. W. Taylor: A comparison of univariate time series methods for forecasting intraday arrivals at a call center. Management Sci. 54 (2008), 253-265. DOI 10.1287/mnsc.1070.0786 | Zbl 1232.90214
[14] P. R. Winters: Forecasting sales by exponentially weighted moving averages. Management Sci. 6 (1960), 324-342. DOI 10.1287/mnsc.6.3.324 | MR 0112740 | Zbl 0995.90562
[15] D. J. Wright: Forecasting data published at irregular time intervals using extension of Holt's method. Management Sci. 32 (1986), 499-510. DOI 10.1287/mnsc.32.4.499
Partner of
EuDML logo