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Optimality and robustness of combinations of moving averages

Author

Listed:
  • J E Boylan

    (Buckinghamshire Chilterns University College)

  • F R Johnston

    (University of Warwick)

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.

Suggested Citation

  • J E Boylan & F R Johnston, 2003. "Optimality and robustness of combinations of moving averages," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 109-115, January.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:1:d:10.1057_palgrave.jors.2601472
    DOI: 10.1057/palgrave.jors.2601472
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    References listed on IDEAS

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    1. F R Johnston & J E Boyland & M Meadows & E Shale, 1999. "Some properties of a simple moving average when applied to forecasting a time series," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1267-1271, December.
    2. F R Johnston & J E Boylan & E Shale & M Meadows, 1999. "A robust forecasting system, based on the combination of two simple moving averages," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1199-1204, December.
    3. Satchell, Steve & Timmermann, Allan, 1995. "On the optimality of adaptive expectations: Muth revisited," International Journal of Forecasting, Elsevier, vol. 11(3), pages 407-416, September.
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    Cited by:

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