Title: Fully Continuous Gated Recurrent Units For processing Time Series. Abstract: For a long time, RNN-based models, such as RNNs, LSTMs, and GRUs, have been used to process time series data. However, RNN-based models do not fit well with real-world sporadically observed data. As a result, many researchers have suggested various enhancements to overcome the limitation. Among them, differential equation-based models, e.g., GRU-ODE-Bayes, ODE-RNN, and so forth, show good accuracy in many cases. Those methods try to continuously model the hidden state of RNNs (or GRUs). However, existing methods' hidden states are piece-wise continuous. In this paper, we represent GRUs as delay differential equations and present fully continuous GRUs. To our knowledge, we propose the first model that continuously generalizes all the parts of GRUs, including their hidden state and various gates. After reconstructing a continuous path $x(t)$ from discrete time series observations $\{(x_i, t_i)\}_{i=0}^{N-1}$ (with an appropriate interpolation algorithm), we calculate the time derivatives of the reset gate $r(t)$, the update gate $z(t)$, the update vector $g(t)$, and the hidden state $h(t)$. Then, we develop an augmented delay differential equation (DDE) that continuously generalizes all the parts. In our experiments with 3 real-world datasets and 13 baselines, our fully continuous GRU method outperforms existing baselines by non-trivial margins. 