Time series forecasting has been an essential field in many different application areas, including economic analysis, meteorology, and so forth. The majority of time series forecasting models are trained using the mean squared error (MSE). However, this training based on MSE causes a limitation known as prediction delay. The prediction delay, which implies the ground-truth precedes the prediction, can cause serious problems in a variety of fields, e.g., finance and weather forecasting -- as a matter of fact, predictions succeeding ground-truth observations are not practically meaningful although their MSEs can be low. This paper proposes a new perspective on traditional time series forecasting tasks and introduces a new solution to mitigate the prediction delay. We introduce a continuous-time gated recurrent unit (GRU) based on the neural ordinary differential equation (NODE) which can supervise explicit time-derivatives. We generalize the GRU architecture in a continuous-time manner and minimize the prediction delay through our time-derivative regularization. Our method outperforms in metrics such as MSE, Dynamic Time Warping (DTW) and Time Distortion Index (TDI). In addition, we demonstrate the low prediction delay of our method in a variety of datasets.

传统时间序列预测任务的新视角和通过时间导数正则化减小预测延迟的一种新解决方案。采用基于神经元常微分方程的连续时间门控循环单元（GRU）可以监督显式的时间导数，方法在MSE、动态时间规整和时间扭曲指数等指标上优于其他方法，并在多个数据集中展示了低预测延迟的特点。

处理时间序列预测中的预测延迟：采用导数正则化的连续GRU方法