DeepPIPE: A distribution-free uncertainty quantification approach for time series forecasting

Time series forecasting is a challenging task as the underlying data generating process is dynamic, nonlinear, and uncertain. Deep learning such as LSTM and auto-encoder can learn representations automatically and has attracted considerable attention in time series forecasting. However, current approaches mainly focus on point estimation, which leads to the inability to quantify uncertainty. Meantime, existing deep uncertainty quantification methods suffer from various limitations in practice. To this end, this paper presents a novel end-to-end framework called deep prediction interval and point estimation (DeepPIPE) that simultaneously performs multi-step point estimation and uncertainty quantification for time series forecasting. The merits of this approach are threefold: first, it requires no prior assumption on the distribution of data noise; second, it utilizes a novel hybrid loss function that improves the accuracy and stability of forecasting; third, it is only optimized by back-propagation algorithm, which is time friendly and easy to be implemented. Experimental results demonstrate that the proposed approach achieves state-of-the-art performance on three real-world datasets.