Temporal hierarchies with autocorrelation for load forecasting

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

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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
Volume280
Pages (from-to)876-888
ISSN0377-2217
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

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

Cite this

@article{6eb9b0517f5641db8573f07bd83ab56e,
title = "Temporal hierarchies with autocorrelation for load forecasting",
abstract = "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.",
keywords = "Autocorrelation, Forecast combination, Forecasting, Reconciliation, Temporal aggregation",
author = "Peter Nystrup and Erik Lindstr{\"o}m and Pierre Pinson and Henrik Madsen",
year = "2020",
month = "1",
day = "1",
doi = "10.1016/j.ejor.2019.07.061",
language = "English",
volume = "280",
pages = "876--888",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier",

}

Temporal hierarchies with autocorrelation for load forecasting. / Nystrup, Peter; Lindström, Erik; Pinson, Pierre; Madsen, Henrik.

In: European Journal of Operational Research, Vol. 280, 01.01.2020, p. 876-888.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Temporal hierarchies with autocorrelation for load forecasting

AU - Nystrup, Peter

AU - Lindström, Erik

AU - Pinson, Pierre

AU - Madsen, Henrik

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Autocorrelation

KW - Forecast combination

KW - Forecasting

KW - Reconciliation

KW - Temporal aggregation

U2 - 10.1016/j.ejor.2019.07.061

DO - 10.1016/j.ejor.2019.07.061

M3 - Journal article

VL - 280

SP - 876

EP - 888

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

ER -