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A note on forecasting demand using the multivariate exponential smoothing framework

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  • Poloni, Federico
  • Sbrana, Giacomo

Abstract

Simple exponential smoothing is widely used in forecasting economic time series. This is because it is quick to compute and it generally delivers accurate forecasts. On the other hand, its multivariate version has received little attention due to the complications arising with the estimation. Indeed, standard multivariate maximum likelihood methods are affected by numerical convergence issues and bad complexity, growing with the dimensionality of the model. In this paper, we introduce a new estimation strategy for multivariate exponential smoothing, based on aggregating its observations into scalar models and estimating them. The original high-dimensional maximum likelihood problem is broken down into several univariate ones, which are easier to solve. Contrary to the multivariate maximum likelihood approach, the suggested algorithm does not suffer heavily from the dimensionality of the model. The method can be used for time series forecasting. In addition, simulation results show that our approach performs at least as well as a maximum likelihood estimator on the underlying VMA(1) representation, at least in our test problems.

Suggested Citation

  • Poloni, Federico & Sbrana, Giacomo, 2015. "A note on forecasting demand using the multivariate exponential smoothing framework," International Journal of Production Economics, Elsevier, vol. 162(C), pages 143-150.
    • Handle: RePEc:eee:proeco:v:162:y:2015:i:c:p:143-150
    DOI: 10.1016/j.ijpe.2015.01.017
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    1. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Forecasting aggregate demand: Analytical comparison of top-down and bottom-up approaches in a multivariate exponential smoothing framework," International Journal of Production Economics, Elsevier, vol. 146(1), pages 185-198.
    2. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    3. Christian Kascha, 2012. "A Comparison of Estimation Methods for Vector Autoregressive Moving-Average Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 297-324.
    4. Moon, Seongmin & Simpson, Andrew & Hicks, Christian, 2013. "The development of a classification model for predicting the performance of forecasting methods for naval spare parts demand," International Journal of Production Economics, Elsevier, vol. 143(2), pages 449-454.
    5. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    6. Shiqing Ling & Michael McAleer, 2010. "A general asymptotic theory for time‐series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 97-111, February.
    7. Ord, Keith & Hibon, Michele & Makridakis, Spyros, 2000. "The M3-Competition1," International Journal of Forecasting, Elsevier, vol. 16(4), pages 433-436.
    8. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    9. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    10. Holt, Charles C., 2004. "Author's retrospective on 'Forecasting seasonals and trends by exponentially weighted moving averages'," International Journal of Forecasting, Elsevier, vol. 20(1), pages 11-13.
    11. Chen, Argon & Blue, Jakey, 2010. "Performance analysis of demand planning approaches for aggregating, forecasting and disaggregating interrelated demands," International Journal of Production Economics, Elsevier, vol. 128(2), pages 586-602, December.
    12. Moon, Seongmin & Hicks, Christian & Simpson, Andrew, 2012. "The development of a hierarchical forecasting method for predicting spare parts demand in the South Korean Navy—A case study," International Journal of Production Economics, Elsevier, vol. 140(2), pages 794-802.
    13. Zotteri, Giulio & Kalchschmidt, Matteo & Caniato, Federico, 2005. "The impact of aggregation level on forecasting performance," International Journal of Production Economics, Elsevier, vol. 93(1), pages 479-491, January.
    14. Dekker, Mark & van Donselaar, Karel & Ouwehand, Pim, 2004. "How to use aggregation and combined forecasting to improve seasonal demand forecasts," International Journal of Production Economics, Elsevier, vol. 90(2), pages 151-167, July.
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    Cited by:

    1. Sbrana, Giacomo & Silvestrini, Andrea & Venditti, Fabrizio, 2017. "Short-term inflation forecasting: The M.E.T.A. approach," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1065-1081.
    2. Poloni, Federico & Sbrana, Giacomo, 2019. "Closed-form results for vector moving average models with a univariate estimation approach," Econometrics and Statistics, Elsevier, vol. 10(C), pages 27-52.

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