Thesis title: Hierarchical forecasting: a network-based approach with applications to multi-hierarchies
In recent years, there has been an increasing interest in forecast reconciliation for hierarchies of time series. This research topic has at its core the simple idea that observed responses at each level of a hierarchy will always add up to the observed responses at higher levels of the same hierarchy. Within this context, numerous approaches in the literature attempt to make predictions coherent and adapted to a given hierarchy: the challenge is to exploit the typically high signal-to-noise ratio that characterizes the most aggregated data to boost the predictive performance on the more granular data.
This dissertation explores different approaches for reconciliation, providing a new application on the Italian Covid-19 dataset to perform a comparative study: the results show that the reconciliation step improves the forecast quality at the bottom level of Italy’s administrative structure.
In addition to this application, a new family of techniques is developed in order to solve the forecast reconciliation problem in a multi-hierarchical scenario, embracing both temporal and classical hierarchies. The idea is to leverage Convolutional Neural Networks (CNN) to obtain consistent and accurate predictions using information at different levels of the hierarchy. More in particular, the proposed architecture generalizes the convolutional approach to work in cases where more than one hierarchy is available, to make all the hierarchies simultaneously consistent. Different implementations of this method are provided in which convolutions are built based on Graph Neural Network or on a multi-channel kind of matrix.
The proposed approach has been tested on different datasets (real and simulated), and the results show that the new architectures achieve promising results that will be further investigated in future research.