Temporal hierarchies with autocorrelation for load forecasting

We propose three 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 estimator facilitates information sharing between aggregation levels using a sparse representation of the inverse autocorrelation matrix. We demonstrate the usefulness of the proposed estimators through an application to short-term electricity load forecasting in different price areas in Sweden. We find that by taking account of the autocovariance when reconciling forecasts, accuracy can be significantly improved uniformly across all frequencies and areas.