Dimensionality reduction in forecasting with temporal hierarchies

Peter Nystrup*, Erik Lindström, Jan K. Møller, Henrik Madsen

*Corresponding author for this work

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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 a temporal hierarchy, which can easily be of very large dimension, yet it is difficult to know a priori which part of the error structure is most important. To address these issues, we propose to use eigendecomposition for dimensionality reduction when reconciling forecasts to extract as much information as possible from the error structure given the data available. We evaluate the proposed estimator in a simulation study and demonstrate its usefulness through applications to short-term electricity load and financial volatility forecasting. We find that accuracy can be improved uniformly across all aggregation levels, as the estimator achieves state-of-the-art accuracy while being applicable to hierarchies of all sizes.

Original languageEnglish
JournalInternational Journal of Forecasting
Issue number3
Pages (from-to)1127-1146
Publication statusPublished - 2021

Bibliographical note

Funding Information:
This work was supported by Vergstiftelsen and the Centre for IT-Intelligent Energy Systems (CITIES) project funded in part by Innovation Fund Denmark under Grant No. 1305-00027B . We thank an Associate Editor and two anonymous reviewers for helpful comments.

Publisher Copyright:
© 2020 The Author(s)


  • Load forecasting
  • Realized volatility
  • Reconciliation
  • Shrinkage
  • Spectral decomposition
  • Temporal aggregation


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