Probabilistic Multi-Step-Ahead Short-Term Water Demand Forecasting with Lasso

Abstract

Water demand is a highly important variable for operational control and decision making. Therefore, the development of accurate forecasts is a valuable field of research to further improve the efficiency of water utilities. Focusing on probabilistic multi-step-ahead forecasting, a time series model is introduced to capture typical autoregressive, calendar, and seasonal effects; to account for time-varying variance; and to quantify the uncertainty and path-dependency of the water demand process. To deal with the high complexity of the water demand process, a high-dimensional feature space is applied, which is efficiently tuned by an automatic shrinkage and selection operator (lasso). It allows to obtain an accurate, simple interpretable and fast computable forecasting model, which is well suited for real-time applications. The complete probabilistic forecasting framework allows not only for simulating the mean and the marginal properties, but also the correlation structure between hours within the forecasting horizon. For practitioners, complete probabilistic multi-step-ahead forecasts are of considerable relevance as they provide additional information about the expected aggregated or cumulative water demand, so that a statement can be made about the probability with which a water storage capacity can guarantee the supply over a certain period of time. This information allows to better control storage capacities and to better ensure the smooth operation of pumps. To appropriately evaluate the forecasting performance of the considered models, the energy score (ES) as a strictly proper multidimensional evaluation criterion, is introduced. The methodology is applied to the hourly water demand data of a German water supplier.