This paper proposes a three-step approach to forecasting time series of electricity consumption at different levels of household aggregation. These series are linked by hierarchical constraints—global consumption is the sum of regional consumption, for example. First, benchmark forecasts are generated for all series using generalized additive models. Second, for each series, the aggregation algorithm ML-Poly, introduced by Gaillard, Stoltz, and van Erven in 2014, finds an optimal linear combination of the benchmarks. Finally, the forecasts are projected onto a coherent subspace to ensure that the final forecasts satisfy the hierarchical constraints. By minimizing a regret criterion, we show that the aggregation and projection steps improve the root mean square error of the forecasts. Our approach is tested on household electricity consumption data; experimental results suggest that successive aggregation and projection steps improve the benchmark forecasts at different levels of household aggregation.

本文提出了一种三步法来预测不同家庭聚集水平的电力消耗时间序列。这些系列通过层次约束联系起来——例如，全球消费是区域消费的总和。首先，使用广义可加模型为所有系列生成基准预测。其次，对于每个系列，Gaillard、Stoltz 和 van Erven 在 2014 年引入的聚合算法 ML-Poly 会找到基准的最佳线性组合。最后，预测被投影到一个连贯的子空间，以确保最终的预测满足层次约束。通过最小化后悔标准，我们表明聚合和投影步骤改善了预测的均方根误差。我们的方法在家庭用电量数据上进行了测试；