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Some properties of a simple moving average when applied to forecasting a time series

Author

Listed:
  • F R Johnston

    (University of Warwick)

  • J E Boyland

    (Buckinghamshire University College)

  • M Meadows

    (University of Warwick)

  • E Shale

    (University of Warwick)

Abstract

Simple (equally weighted) moving averages are frequently used to estimate the current level of a time series, with this value being projected as a forecast for future observations. A key measure of the effectiveness of the method is the sampling error of the estimator, which this paper defines in terms of characteristics of the data. This enables the optimal length of the average for any steady state model to be established and the lead time forecast error derived. A comparison of the performance of a simple moving average (SMA) with an exponentially weighted moving average (EWMA) is made. It is shown that, for a steady state model, the variance of the forecast error is typically less than 3% higher than the appropriate EWMA. This relatively small difference may explain the inconclusive results from the empirical studies about the relative predictive performance of the two methods.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:12:d:10.1057_palgrave.jors.2600823
    DOI: 10.1057/palgrave.jors.2600823
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    Citations

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    Cited by:

    1. Dmitrii Tverdyi & Evgeny Makarov & Roman Parovik, 2023. "Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    2. Dimitrios Kontogiannis & Dimitrios Bargiotas & Aspassia Daskalopulu & Lefteri H. Tsoukalas, 2021. "A Meta-Modeling Power Consumption Forecasting Approach Combining Client Similarity and Causality," Energies, MDPI, vol. 14(19), pages 1-19, September.
    3. Tliche, Youssef & Taghipour, Atour & Canel-Depitre, Béatrice, 2020. "An improved forecasting approach to reduce inventory levels in decentralized supply chains," European Journal of Operational Research, Elsevier, vol. 287(2), pages 511-527.
    4. 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.
    5. S. M. Masrur Ahmed, 2023. "Sizing Strategies for Algorithmic Trading in Volatile Markets: A Study of Backtesting and Risk Mitigation Analysis," Papers 2309.09094, arXiv.org, revised Sep 2023.
    6. Che-Yu Hung & Chien-Chih Wang & Shi-Woei Lin & Bernard C. Jiang, 2022. "An Empirical Comparison of the Sales Forecasting Performance for Plastic Tray Manufacturing Using Missing Data," Sustainability, MDPI, vol. 14(4), pages 1-21, February.
    7. E A Shale & J E Boylan & F R Johnston, 2006. "Forecasting for intermittent demand: the estimation of an unbiased average," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 588-592, May.
    8. Fernandes, Betina & Street, Alexandre & Valladão, Davi & Fernandes, Cristiano, 2016. "An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets," European Journal of Operational Research, Elsevier, vol. 255(3), pages 961-970.
    9. Strijbosch, Leo W.G. & Syntetos, Aris A. & Boylan, John E. & Janssen, Elleke, 2011. "On the interaction between forecasting and stock control: The case of non-stationary demand," International Journal of Production Economics, Elsevier, vol. 133(1), pages 470-480, September.

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