Abstract: Hierarchical time series involve multiple time series with hierarchical constraints,where the data of the upper-level nodes are the cumulative sum of all their child node data.The main challenge in hierarchical time series forecasting is to accurately predict each series while ensuring consistency across different levels,i.e.,the forecast must satisfy the additive constraints within the hierarchical structure.With the emergence of large-scale data,this complex and challenging problem has demonstrated greater research value and a broad range of application prospects.This study reviews the literature on hierarchical time series forecasting methods,summarizing and generalizing from the aspects of classification methods and theoretical applications,while also discussing the challenges faced by this technology and the gaps in practical applications.The analysis indicates that hierarchical time series forecasting methods can mainly be divided into two stages,which are forecasting models and revision models,gradually introducing machine learning and deep learning methods,and evolving into end-to-end methods that integrate forecasting and revision models.These methods are widely applied in the fields of business operations and government governance.In terms of future research trends,the first area of focus should be the impact of massive data on the accuracy of two-stage method forecasts,followed by in-depth research on end-to-end hierarchical time series forecasting models to avoid the issue of non-coherent parameters between stages.Additionally,research in government management and business operations can focus on modeling the differences in attention levels at various hierarchical levels caused by specific issues.

Key words: Hierarchical time series forecasting, Consistency, Machine learning, Deep learning