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Temporal hierarchies with autocorrelation for load forecasting

Nystrup, Peter LU orcid ; Lindström, Erik LU orcid ; Pinson, Pierre and Madsen, Henrik (2020) In European Journal of Operational Research 280(3). p.876-888
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... (More)

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.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Autocorrelation, Forecast combination, Forecasting, Reconciliation, Temporal aggregation
in
European Journal of Operational Research
volume
280
issue
3
pages
13 pages
publisher
Elsevier
external identifiers
  • scopus:85070508120
ISSN
0377-2217
DOI
10.1016/j.ejor.2019.07.061
language
English
LU publication?
yes
id
d0fa459b-874b-40b6-aed4-a1423e5dcff8
date added to LUP
2019-08-27 09:47:09
date last changed
2023-11-19 12:35:14
@article{d0fa459b-874b-40b6-aed4-a1423e5dcff8,
  abstract     = {{<p>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.</p>}},
  author       = {{Nystrup, Peter and Lindström, Erik and Pinson, Pierre and Madsen, Henrik}},
  issn         = {{0377-2217}},
  keywords     = {{Autocorrelation; Forecast combination; Forecasting; Reconciliation; Temporal aggregation}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{876--888}},
  publisher    = {{Elsevier}},
  series       = {{European Journal of Operational Research}},
  title        = {{Temporal hierarchies with autocorrelation for load forecasting}},
  url          = {{http://dx.doi.org/10.1016/j.ejor.2019.07.061}},
  doi          = {{10.1016/j.ejor.2019.07.061}},
  volume       = {{280}},
  year         = {{2020}},
}