Joint Forecasting Of Hierarchical Time Series Based On Multi-task Learning

Hierarchical time series refers to a set of time series that are limited by the aggregation relationship.Hierarchical forecasting has been widely used in statistics and economics such as electricity demand forecasting,tourism quantity forecasting and commercial tax forecasting.Existing hierarchical forecasting methods are usually based on a ”two-step” strategy.Firstly,all time series in the hierarchy are forecasted independently,and then different reconciled algorithms are adopted to satisfy the aggregation consistency.However,the ”two-step” methods are time-consuming and does not ensure that the forecasts of all time series are overall optimal.In order to solve the above problems,joint forecasting models of hierarchical time series are proposed in this paper.The main work and innovations are as follows:(1)Hierarchical joint forecasting based on multi-task linear regression.Based on multi-task learning,a linear regression model that integrates all the bottom series features and hierarchical structure is constructed in this paper.The model could simultaneously output forecasts for all time series and satisfy the requirements for aggregation consistency.By using the correlation between time series and optimizing a global loss function,the forecasting results could be optimized overall.In order to avoid the dimensionality disaster caused by the increase of the number of time series,a sparse model with group sparsity and element sparsity constraints was further learned according to the data characteristics.Experimental results on simulation data and tourism data show that the joint forecasting model has a better performance while simplifying the forecasting process.(2)Hierarchical joint forecasting based on multi-task deep learning.The deep learning model proposed in this paper takes the bottom series in the hierarchy as multi task input,extracts the local correlation among the bottom series through the convolution neural network,and the short-term and long-term dependence patterns through recurrent neural network.At the same time,the traditional autoregressive linear model is incorporated,which makes the nonlinear deep learning model more robust to time series with large scale changes.According to the bottom series errors and the hierarchy matrix,the paper creates a global loss function that contains all series errors.Based on the well-fitting learning characteristics of deep learning,the long-term electricity demand series with complex periodicity is modeled.The experimental results show that the performance is significantly improved compared with the traditional methods.