  Large collections of time series data are often organized into hierarchies
with different levels of aggregation; examples include product and geographical
groupings. Probabilistic coherent forecasting is tasked to produce forecasts
consistent across levels of aggregation. In this study, we propose to augment
neural forecasting architectures with a coherent multivariate mixture output.
We optimize the networks with a composite likelihood objective, allowing us to
capture time series' relationships while maintaining high computational
efficiency. Our approach demonstrates 13.2% average accuracy improvements on
most datasets compared to state-of-the-art baselines. We conduct ablation
studies of the framework components and provide theoretical foundations for
them. To assist related work, the code is available at this
https://github.com/Nixtla/neuralforecast.
