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M5 competition uncertainty: Overdispersion, distributional forecasting, GAMLSS, and beyond

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  • Ziel, Florian

Abstract

The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data face strong overdispersion and sporadic demand, especially zero demand. We discuss modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fail to address the data characteristics, due to the considered objective functions. Distributional forecasting provides a suitable modeling approach to overcome those problems. The GAMLSS framework allows for flexible probabilistic forecasting using low-dimensional distributions. We illustrate how the GAMLSS approach can be applied to M5 competition data by modeling the location and scale parameters of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawbacks, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.

Suggested Citation

  • Ziel, Florian, 2022. "M5 competition uncertainty: Overdispersion, distributional forecasting, GAMLSS, and beyond," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1546-1554.
    • Handle: RePEc:eee:intfor:v:38:y:2022:i:4:p:1546-1554
    DOI: 10.1016/j.ijforecast.2021.09.008
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    2. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    3. Salinas, David & Flunkert, Valentin & Gasthaus, Jan & Januschowski, Tim, 2020. "DeepAR: Probabilistic forecasting with autoregressive recurrent networks," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1181-1191.
    4. Ulrich, Matthias & Jahnke, Hermann & Langrock, Roland & Pesch, Robert & Senge, Robin, 2021. "Distributional regression for demand forecasting in e-grocery," European Journal of Operational Research, Elsevier, vol. 294(3), pages 831-842.
    5. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    6. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    7. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    8. Haben, Stephen & Giasemidis, Georgios, 2016. "A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1017-1022.
    9. Micha{l} Narajewski & Florian Ziel, 2020. "Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories," Papers 2005.01365, arXiv.org, revised Aug 2020.
    10. Narajewski, Michał & Ziel, Florian, 2020. "Ensemble forecasting for intraday electricity prices: Simulating trajectories," Applied Energy, Elsevier, vol. 279(C).
    11. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.
    12. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    13. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    Cited by:

    1. Simon Hirsch & Florian Ziel, 2023. "Multivariate Simulation-based Forecasting for Intraday Power Markets: Modelling Cross-Product Price Effects," Papers 2306.13419, arXiv.org.

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    More about this item

    Keywords

    M5 competition; Probabilistic forecasting; GAMLSS; Distribution modeling; Overdispersion; Count data; Demand forecasting;
    All these keywords.

    JEL classification:

    • M5 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics

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