Biased Resampling Strategies for Imbalanced SpatioTemporal Forecasting Extreme and rare events, such as abnormal spikes in air pollution or weather conditions can have serious repercussions. Many of these sorts of events develop from spatiotemporal processes, and accurate predictions are a most valuable tool in addressing their impact, in a timely manner. In this paper, we propose a new set of resampling strategies for imbalanced spatiotemporal forecasting tasks, by introducing bias into formerly random processes. This spatiotemporal bias includes a hyperparameter that regulates the relative importance of the temporal and spatial dimensions in the selection of observations during underor oversampling. We test and compare our proposals against standard versions of the strategies on 10 different georeferenced numeric time series, using 3 distinct offtheshelf learning algorithms. Experimental results show that our proposal provides an advantage over random resampling strategies in imbalanced spatiotemporal forecasting tasks. Additionally, we also find that valuing an observationu0027s recency is more useful when oversampling; while valuing its spatial distance to other cases with extreme values is more beneficial when undersampling.

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 firstorder 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 shortterm 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. (Less)