The M5 Competition is the 5th Iteration of the M series of Forecasting competitions from the University of Nicosia. For this iteration, Walmart sales at different scales (from item-level to overall) are to be predicted, for a total of 42,840 different time series to be predicted. The competition was divided into two parts: Accuracy and Uncertainty. For the accuracy part, point estimates are to be evaluated while uncertainty quantiles will be evaluated for the uncertainty part.
For this competition, I used the FFORMA (short for Feature-based forecast model averaging)
meta-learning approach as described in
Montero Manso et al.'s paper.
This method aims to train a meta-learner that learns the appropriate weights to be given
to each individual model forecast. Since we are also interested on the uncertainty quantiles,
we want to optimize the forecast loss:
Where 
is the loss at time step 
, for individual model 
and 
is the weight function with predictors 
.
The meta-learner that was used was a tree-based gradient boosting
algorithm. I trained one gradient boosting model for each quantile.
See paper and code for more details on the implementation.
Hyperparameters for the gradient boosting algorithm chosen were the following:
| Parameter | Value |
|---|---|
| Max depth | 4 |
| learning rate | 0.114 |
| Subsampling prop | 0.9 |
| colsample by tree | 0.6 |