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Dimensionality reduction in forecasting with temporal hierarchies

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  • Nystrup, Peter
  • Lindström, Erik
  • Møller, Jan K.
  • Madsen, Henrik
Abstract
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.

Suggested Citation

  • Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
    • Handle: RePEc:eee:intfor:v:37:y:2021:i:3:p:1127-1146
    DOI: 10.1016/j.ijforecast.2020.12.003
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    Cited by:

    1. Zhang, Bohan & Kang, Yanfei & Panagiotelis, Anastasios & Li, Feng, 2023. "Optimal reconciliation with immutable forecasts," European Journal of Operational Research, Elsevier, vol. 308(2), pages 650-660.
    2. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    3. Mikkel L. Sørensen & Peter Nystrup & Mathias B. Bjerregård & Jan K. Møller & Peder Bacher & Henrik Madsen, 2023. "Recent developments in multivariate wind and solar power forecasting," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 12(2), March.
    4. Bergsteinsson, Hjörleifur G. & Møller, Jan Kloppenborg & Nystrup, Peter & Pálsson, Ólafur Pétur & Guericke, Daniela & Madsen, Henrik, 2021. "Heat load forecasting using adaptive temporal hierarchies," Applied Energy, Elsevier, vol. 292(C).

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