  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.
