Temporal hierarchies with autocorrelation for load forecasting

Peter Nystrup*, Erik Lindström, Pierre Pinson, Henrik Madsen

*Corresponding author for this work

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We propose four different estimators that take into account the autocorrelation structure when reconciling forecasts in a temporal hierarchy. 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. In previous studies, weights assigned to the forecasts were given by the structure of the hierarchy or the forecast error variances without considering potential autocorrelation in the forecast errors. Our first estimator considers the autocovariance matrix within each aggregation level. Since this can be difficult to estimate, we propose a second estimator that blends autocorrelation and variance information, but only requires estimation of the first-order autocorrelation coefficient at each aggregation level. Our third and fourth estimators facilitate information sharing between aggregation levels using robust estimates of the cross-correlation matrix and its inverse. We compare the proposed estimators in a simulation study and demonstrate their usefulness through an application to short-term electricity load forecasting in four price areas in Sweden. We find that by taking account of auto- and cross-covariances when reconciling forecasts, accuracy can be significantly improved uniformly across all frequencies and areas.

Original languageEnglish
JournalEuropean Journal of Operational Research
Pages (from-to)876-888
Publication statusPublished - 1 Jan 2020


  • Autocorrelation
  • Forecast combination
  • Forecasting
  • Reconciliation
  • Temporal aggregation


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