Journal of the Operational Research Society

, Volume 54, Issue 1, pp 109–115

Optimality and robustness of combinations of moving averages

Theoretical Paper

Abstract

A combination of moving averages has been shown previously to be more accurate than simple moving averages, under certain conditions, and to be more robust to non-optimal parameter specification. However, the use of the method depends on specification of three parameters: length of greater moving average, length of shorter moving average, and the weighting given to the former. In this paper, expressions are derived for the optimal values of the three parameters, under the conditions of a steady state model. These expressions reduce a three-parameter search to a single-parameter search. An expression is given for the variance of the sampling error of the optimal combination of moving averages and this is shown to be marginally greater than that for exponentially weighted moving averages (EWMA). Similar expressions for optimal parameters and the resultant variance are derived for equally weighted combinations. The sampling variance of the mean of such combinations is shown to be almost identical to the optimal general combination, thus simplifying the use of combinations further. It is demonstrated that equal weight combinations are more robust than EWMA to noise to signal ratios lower than expected, but less robust to noise to signal ratios higher than expected.

Keywords

forecasting time-series moving averages combinations of forecasts exponentially weighted moving averages 

References

  1. Johnston FR, Boylan JE, Shale E, Meadows M (1999). A robust forecasting system, based on the combination of two simple moving averages. J Opl Res Soc 50: 1199–1204.CrossRefGoogle Scholar
  2. Johnston FR, Boylan JE, Meadows M, Shale E (1999). Some properties of a simple moving average when applied to forecasting a time series. J Opl Res Soc 50: 1267–1271.CrossRefGoogle Scholar
  3. Muth JF (1960). Optimal properties of exponentially weighted forecasts. J Am Statist Assoc 55: 299–306.CrossRefGoogle Scholar
  4. Satchell S, Timmermann A (1995). On the optimality of adaptive expectations: Muth revisited. Int J Forecasting 11: 407–416.CrossRefGoogle Scholar
  5. Johnston FR, Harrison PJ (1984). Discount weighted moving averages. J Opl Res Soc 35: 629–635.CrossRefGoogle Scholar
  6. Gardner ES, Dannenbring DG (1980). Forecasting with exponential smoothing: some guidelines for model selection. Decision Sci 11: 370–383.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2003

Authors and Affiliations

  1. 1.Buckinghamshire Chilterns University CollegeUK
  2. 2.University of WarwickUK

Personalised recommendations