Title: Probabilistic forecasts in hierarchical time series
Authors: Puwasala Gamakumara - Monash University (Australia) [presenting]
Anastasios Panagiotelis - Monash University (Australia)
George Athanasopoulos - Monash University (Australia)
Rob Hyndman - Monash University (Australia)
Abstract: Forecasting hierarchical time series has been of great interest in many applications. While there is a rich literature on hierarchical point forecasting, we focus on a probabilistic hierarchical framework. We initially provide a theoretical foundation for probabilistic forecast reconciliation by considering the aggregation structure of a hierarchy. We observe that the trace minimization (MinT) approach in producing optimal point forecasts, is also generating optimal probabilistic forecasts under Gaussianity. We further relax the Gaussian assumption and propose a novel, non-parametric approach. This involves first simulating future sample paths of the whole hierarchy using bootstrapped training errors and then reconciling these sample paths so that they become coherent. We evaluate both the MinT Gaussian and non-parametric bootstrap approaches via extensive Monte Carlo simulations.