## 3 Methodology
### Mc-Tcgrul
#### 3.2.2 TCGRU  
The gated recurrent unit (GRU) is a type of neural network with an input-output architecture similar to that of RNNs. It addresses the problem of long-term dependencies by incorporating a gating mechanism, inspired by the LSTM network [34]. The GRUmodel includes two key components: the update gate and the reset gate. The update gate determines what information to discard and what to add, thus controlling the extent to which information from the previous time step is preserved in the current state. The reset gate governs how the current input and previous information are combined, determining how much of the past information should be forgotten. The update gate in GRU serves a function similar to the combination of the forget gate and input gate in LSTM, but it provides a more convenient way to balance information retention and forgetting. The basic structure of the GRU network unit is illustrated in Figure 2.  
The formulas for calculating \(z_{t}\), \(r_{t}\), \(\overset{\sim}{h}_{t}\), and \(h_{t}\) are as follows:  
\[z_{t}=\sigma(W_{z}\cdot[h_{t-1},x_{t}]) \tag{11}\]  
\[r_{t}=\sigma(W_{r}\cdot[h_{t-1},x_{t}]) \tag{12}\]  
\[\overset{\sim}{h}_{t}=tanh(W\cdot[r_{t}*h_{t-1},x_{t}]) \tag{13}\]  
\[h_{t}=(1-z_{t})*h_{t-1}+z_{t}*\overset{\sim}{h}_{t} \tag{14}\]  
The variable \(z_{t}\) represents the computation performed by the update gate, \(r_{t}\) corresponds to the operation in the reset gate, and \(h_{t}\) is the final retained information. These formulas are interrelated, enabling the GRU network to balance information retention and discarding, all while having fewer parameters compared to the LSTM network. The temporal convolutional network (TCN) is a neural network model designed for handling time-series data [35]. It combines the parallel computational advantages of traditional convolutional neural networks with the specific requirements of time-based tasks, effectively preventing information leakage. The TCN primarily utilizes causal convolutions, dilated convolutions, and residual connections. In the TCN model, a 1D fully convolutional network architecture is first used, where the length of the hidden layers matches that of the input layer. Zero padding is applied to ensure that the data length remains consistent between layers. To avoid information leakage, the TCN employs causal convolutions, where the output at time \(t\) depends only on the inputs at t and earlier times. However, when dealing with long time-series data, this structure needs a deep network, which increases the computational load. To address this, dilated convolutions are introduced. Dilated convolutions incorporate gaps within the convolutional kernels, enabling spaced data convolution. Given a convolutional kernel size of k and a dilation factor of d, the receptive field size at a given layer relative to the previous layer is \(1+\text{d}\ (\text{k}-1)\). By increasing the kernel size and dilation factor, the receptive field can be expanded, with the dilation factor typically increasing exponentially. This structure allows TCNs to flexibly control the receptive field based on task requirements, enhancing their temporal memory capabilities. When handling complex, long time-series data, TCNs can use residual connection modules to mitigate network degradation. Within a residual block, the TCN includes two  
Figure 2: Structure of the GRU network unit. layers of dilated causal convolutions, along with ReLU activation, weight normalization, and dropout layers. The structure of the TCN residual block is shown in Figure 3.  
Given that a single deep learning network may still have limitations in extracting features from time-series data, model coupling and optimization are employed to enhance the ability to learn core features from deep data layers, thereby improving the accuracy of time-series predictions. This section introduces a short-term LS time-series prediction model, based on time convolution and stacked GRU from deep learning.