Evaluating Point and Probabilistic Forecasts for Intermittent Retail Demand
DOI:
https://doi.org/10.63282/3050-922X.IJERET-V6I2P119Keywords:
Intermittent Demand, Retail Sales, Probabilistic Forecasting, Negative Binomial, Forecast Evaluation, M5, Gradient BoostingAbstract
Forecast comparisons for intermittent retail demand can confound the forecasting method with the statistical quantity being predicted. Absolute error favors a conditional median, whereas squared error favors a conditional mean; these quantities differ substantially when sales are sparse. This study evaluates classical intermittent-demand estimators, rolling-history baselines and a pooled gradient-boosted model on 3,000 M5 item–store series over two successive 28-day test windows. Four predictive distributions provide separately defined means, medians and nine quantiles. The pooled model attains mean RMSSE 0.7669 against 0.7730 for SBA. Its negative binomial configuration attains scaled quantile loss 0.7257 against 0.7400 for SBA with the same distribution family; the paired difference is −0.01425 with a product-cluster bootstrap interval of [−0.02038, −0.00977]. Deriving a median from a distribution improves absolute-error scores without changing its underlying mean forecast. The analysis shows why distributional assumptions, information sets and aggregation choices must be reported alongside accuracy. Forecast accuracy alone does not establish an inventory benefit: that requires a replenishment policy, a lead-time demand distribution and operational cost and service measures.
References
[1] T. Gneiting, “Making and evaluating point forecasts,” Journal of the American Statistical Association, 106(494), 746–762, 2011. doi:10.1198/jasa.2011.r10138.
[2] S. Kolassa, “Evaluating predictive count data distributions in retail sales forecasting,” International Journal of Forecasting, 32(3), 788–803, 2016. doi:10.1016/j.ijforecast.2015.12.004.
[3] S. Makridakis, E. Spiliotis and V. Assimakopoulos, “M5 accuracy competition: Results, findings, and conclusions,” International Journal of Forecasting, 38(4), 1346–1364, 2022. doi:10.1016/j.ijforecast.2021.11.013.
[4] J. D. Croston, “Forecasting and stock control for intermittent demands,” Operational Research Quarterly, 23(3), 289–303, 1972. doi:10.1057/jors.1972.50.
[5] A. A. Syntetos and J. E. Boylan, “The accuracy of intermittent demand estimates,” International Journal of Forecasting, 21(2), 303–314, 2005. doi:10.1016/j.ijforecast.2004.10.001.
[6] R. H. Teunter, A. A. Syntetos and M. Z. Babai, “Intermittent demand: Linking forecasting to inventory obsolescence,” European Journal of Operational Research, 214(3), 606–615, 2011. doi:10.1016/j.ejor.2011.05.018.
[7] A. A. Syntetos, J. E. Boylan and J. D. Croston, “On the categorization of demand patterns,” Journal of the Operational Research Society, 56(5), 495–503, 2005. doi:10.1057/palgrave.jors.2601841.
[8] K. Nikolopoulos, A. A. Syntetos, J. E. Boylan, F. Petropoulos and V. Assimakopoulos, “An aggregate–disaggregate intermittent demand approach (ADIDA) to forecasting: An empirical proposition and analysis,” Journal of the Operational Research Society, 62(3), 544–554, 2011. doi:10.1057/jors.2010.32.
[9] F. Petropoulos and N. Kourentzes, “Forecast combinations for intermittent demand,” Journal of the Operational Research Society, 66(6), 914–924, 2015. doi:10.1057/jors.2014.62.
[10] P. Montero-Manso and R. J. Hyndman, “Principles and algorithms for forecasting groups of time series: Locality and globality,” International Journal of Forecasting, 37(4), 1632–1653, 2021. doi:10.1016/j.ijforecast.2021.03.004.
[11] G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye and T.-Y. Liu, “LightGBM: A highly efficient gradient boosting decision tree,” Advances in Neural Information Processing Systems, 30, 2017.
[12] D. Salinas, V. Flunkert, J. Gasthaus and T. Januschowski, “DeepAR: Probabilistic forecasting with autoregressive recurrent networks,” International Journal of Forecasting, 36(3), 1181–1191, 2020. doi:10.1016/j.ijforecast.2019.07.001.
[13] R. J. Hyndman and A. B. Koehler, “Another look at measures of forecast accuracy,” International Journal of Forecasting, 22(4), 679–688, 2006. doi:10.1016/j.ijforecast.2006.03.001.
[14] S. Makridakis, E. Spiliotis, V. Assimakopoulos, Z. Chen, A. Gaba, I. Tsetlin and R. L. Winkler, “The M5 uncertainty competition: Results, findings and conclusions,” International Journal of Forecasting, 38(4), 1365–1385, 2022. doi:10.1016/j.ijforecast.2021.10.009.
