M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond

TL;DR

This paper addresses the challenges of probabilistic sales forecasting in the M5 competition by highlighting overdispersion and zero demand issues, proposing GAMLSS-based distributional modeling as a flexible solution.

Contribution

It demonstrates the application of GAMLSS for distributional forecasting in retail demand data, overcoming limitations of traditional machine learning methods.

Findings

GAMLSS effectively models overdispersed count data with zero inflation.

Popular ML methods like LightGBM and XGBoost are inadequate for distributional forecasting in this context.

Distributional modeling frameworks offer flexible probabilistic forecasts for complex retail demand data.

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 faces strong overdispersion and sporadic demand, especially zero demand. We discuss resulting 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) fails to address the data characteristics due to the considered objective functions. The distributional forecasting provides a suitable modeling approach for to the overcome those problems. The GAMLSS framework allows flexible probabilistic forecasting using low dimensional distributions. We illustrate, how the GAMLSS approach can be applied for the M5 competition data by modeling the location and scale parameter of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawback, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.