  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.
