Dimensionality reduction in forecasting with temporal hierarchies

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Dimensionality reduction in forecasting with temporal hierarchies. / Nystrup, Peter; Lindström, Erik; Møller, Jan K.; Madsen, Henrik.

In: International Journal of Forecasting, Vol. 37, No. 3, 2021, p. 1127-1146.

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TY - JOUR

T1 - Dimensionality reduction in forecasting with temporal hierarchies

AU - Nystrup, Peter

AU - Lindström, Erik

AU - Møller, Jan K.

AU - Madsen, Henrik

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Load forecasting

KW - Realized volatility

KW - Reconciliation

KW - Shrinkage

KW - Spectral decomposition

KW - Temporal aggregation

U2 - 10.1016/j.ijforecast.2020.12.003

DO - 10.1016/j.ijforecast.2020.12.003

M3 - Article

AN - SCOPUS:85099146966

VL - 37

SP - 1127

EP - 1146

JO - International Journal of Forecasting

JF - International Journal of Forecasting

SN - 1872-8200

IS - 3

ER -