Multi-task Learning Method for Hierarchical Time Series Forecasting

Abstract

Hierarchical time series is a set of time series organized by aggregation constraints and it is widely used in many real-world applications. Usually, hierarchical time series forecasting can be realized with a two-step method, in which all time series are forecasted independently and then the forecasting results are reconciled to satisfy aggregation consistency. However, these two-step methods have a high computational complexity and are unable to ensure optimal forecasts for all time series. In this paper, we propose a novel hierarchical forecasting approach to solve the above problems. Based on multi-task learning, we construct an integrated model that combines features of the bottom level series and the hierarchical structure. Then forecasts of all time series are output simultaneously and they are aggregated consistently. The model has the advantage of utilizing the correlation between time series. And the forecasting results are overall optimal by optimizing a global loss function. In order to avoid the curse of dimensionality as the number of time series grows larger, we further learn a sparse model with group sparsity and element-wise sparsity constraints according to data characteristics. The experimental results on simulation data and tourism data demonstrate that our method has a better overall performance while simplifying forecasting process.