Dimensionality reduction in forecasting with temporal hierarchies

Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. It can be challenging to estimate the full cross-covariance matrix for hierarchy, which easily of very large dimension, yet it is difficult know priori part error structure most important. To address these issues, we propose use eigendecomposition dimensionality reduction when reconciling extract as much possible given data available. We evaluate proposed estimator in simulation study demonstrate its usefulness through applications short-term electricity load financial volatility forecasting. find accuracy improved uniformly across all levels, achieves state-of-the-art being applicable hierarchies sizes.