Optimal reconciliation of hierarchical wind energy forecasts utilizing temporal correlation

Independent wind energy forecasts of a wind farm at different time horizons have limited accuracy, and they show disagreement despite relating to the same wind farm. The limited forecast accuracy is attributable to the insufficient information at a particular time horizon of the wind energy time series, whereas applying distinct forecasting methods to several time series of non-identical patterns at different time scales causes disagreement among forecasts. Mutual disagreement among less accurate forecasts negatively impacts the decision-making capabilities in associated power systems activities at distinct time scales. The configuration of time series expressing different time horizons at different levels of a non-overlapped hierarchically aggregated framework manifests a temporal hierarchy. Forecast combination through reconciliation of time series forecasts drawn at different hierarchical levels of temporal hierarchy using any state-of-the-art method facilitates the sharing of diverse information across the hierarchy; consequently, accuracy and mutual agreement of forecasts improve. Such benefits may be further enhanced by embedding intra- and inter-level forecast error correlations in the forecast reconciliation process. However, the forecast error covariance matrix of temporal hierarchy becomes a complex high-dimensional structure while accommodating intra- and inter-level correlations. Estimating such a matrix is challenging since the high-dimensional structure severely impedes the identifiability of model parameters. Besides, in the hierarchical forecast reconciliation process, the number of predictor variables is generally higher than the number of samples. This condition gives rise to a singular covariance matrix, making it non-invertible, and thus obstructs its parameter estimation. This work employs the MinT(shrinkage) covariance matrix estimator that considers all correlations and shrinks the non-diagonal components of the matrix toward zero to avert the complexity and, therefore, the non-identifiability. Additionally, the shrinkage parameter λ of MinT(shrinkage) conveniently obtains the invertible matrix. The case study validates that while incorporating the intra- and inter-level forecast error correlations, MinT(shrinkage) provides competitively accurate and mutually agreed forecasts over other reconciliation methods.