A novel robust structural quadratic forecasting model and applications

Recently, big data have been collected and stored for the purpose of forecasting in modern operations management. Nevertheless, a massive amount of data information does not provide additional advantages as expected when implementing forecasting or decision-making tasks but causes a waste of time and memory for collection, storage, and computing. Besides hierarchical time series forecasting, strong and weak hierarchies in variable space have also been studied for years. To this end, structural variable selection methods that extract vital information from data by distinguishing important variable from nuisance variable with strong or weak hierarchy are favored by scholars. However, the existing structural variable selection methods focus on establishing models with Gaussian or binomial noises without considering heavy-tailed distributions. Therefore, in this paper, we investigate a robust structured variable selection approach called structural quadratic quantile regression. The model hierarchies are achieved using a proper design of an optimization with check loss function for robustness, regularization term, and one constraint. In computation, a novel algorithm is derived based on Dykstra's algorithm and the proximal alternating direction method of multipliers (pADMM), and its convergence is theoretically guaranteed. Finally, the efficacy of the proposed approach is demonstrated using both simulation and empirical applications from numbers of scientific domains in forecasting.