Regularization in hierarchical time series forecasting with application to electricity smart meter data

Accurate electricity demand forecast plays a key role in sustainable power systems. It enables better decision making in the planning of electricity generation and distribution for many use cases. The electricity demand data can often be represented in a hierarchical structure. For example, the electricity consumption of a whole country could be disaggregated by states, cities, and households. Hierarchical forecasts require not only good prediction accuracy at each level of the hierarchy, but also the consistency between different levels. State-of-the-art hierarchical forecasting methods usually apply adjustments on the individual level forecasts to satisfy the aggregation constraints. However, the high-dimensionality of the unpenalized regression problem and the estimation errors in the high-dimensional error covariance matrix can lead to increased variability in the revised forecasts with poor prediction performance. In order to provide more robustness to estimation errors in the adjustments, we present a new hierarchical forecasting algorithm that computes sparse adjustments while still preserving the aggregation constraints. We formulate the problem as a high-dimensional penalized regression, which can be efficiently solved using cyclical coordinate descent methods. We also conduct experiments using a large-scale hierarchical electricity demand data. The results confirm the effectiveness of our approach compared to state-of-the-art hierarchical forecasting methods, in both the sparsity of the adjustments and the prediction accuracy. The proposed approach to hierarchical forecasting could be useful for energy generation including solar and wind energy, as well as numerous other applications.