## 4 Experiments and Analysis
### Comparative Experiment  
In this study's experimental environment, we trained our model on a platform that included Python 3.11.5, PyTorch 2.11.0, and CUDA 12.1. We configured the hardware with an i5-13490f CPU, a GeForce RTX 4060 ti GPU (8 GB), a 2048 GB hard disk, and 32 GB of RAM, operating on Windows 11 Professional Edition. Table 2 presents the configuration of the parameters in the CT-Transformer model. In CSPNet-Attention, the \"factor\" parameter governs the sparsity of sparse self-attention, determining the maximum relative distance considered for each position. \"Scale\" is an optional factor that adjusts the attention scores and is commonly employed in attention mechanisms to modulate the attention distribution range. \"Dropout rate\" refers to the probability of omitting units during the attention calculation, a regularization strategy designed to prevent model overfitting. In the TCN-LSTM hybrid model, we configured the prediction window to 96/192/336/720, set the learning rate at 0.001 and the dropout rate at 0.05, and conducted 20 training epochs. We chose a batch size of 32, allocated 64 units to the hidden layer, and applied a convolutional layer with a kernel size of 3. Our proposed CT-Transformer model addresses the limitations of traditional forecasting methods in handling non-stationary time series and their significant computational resource consumption. We benchmarked against two advanced state-of-the-art models, NHiTS and SCINet. NHiTS, a neurally-hierarchical interpolated time-series forecasting method, employs multi-rate data sampling, linear projection, and temporal interpolation of the input signal to tackle long-term forecasting challenges. SCINet, employing sample convolution and interactions, introduces a novel method that significantly enhances the efficiency of temporal modeling and forecasting in time-series analysis. This method constructs a binary tree-structured temporal convolutional network, considerably improving temporal data handling. Additionally, for comparison, the study selected four cutting-edge Transformer variants: Autoformer, ETSformer, FEDformer, and GBT. Among these, Autoformer employs autocorrelation decomposition for long-term forecasting, splitting the input series into deep seasonal trends and stochastic fluctuations, and models cyclical dependencies using an autocorrelation attention mechanism. ETSformer integrates exponential smoothing and seasonal-level growth decomposition. FEDformer employs frequency-enhanced decomposition, utilizing Fourier and wavelet transforma \begin{table}
\begin{tabular}{l l} \hline \hline
**Hyper-Parameters/Settings** & **Values** \\ \hline Embedding dimensions of the & 32 \\ Auto-Regression stage & \\ Embedding dimensions of & 32 \\ CSPNet-Attention(factor) & 5 \\ CSPNet-Attention(scale) & None \\ CSPNet-Attention(dropout rate) & 0.1 \\ Self-Regression stage & \\ Kernel size of Conv layers & 3 \\ Input window size & 96/192/336/720 \\ Standardization & Z-score \\ Loss function & MSE \\ Optimizer & Adam \\ Dropout rate & 0.1 \\ Learning rate & \(1\times 10^{-4}\) \\ Learning rate decreasing rate & Half/epoch \\ Batch size & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameters. tions. The GBT (Two-stage Transformer) breaks down the forecasting process into autoregression phases, tackling the disparity in statistical characteristics between input and predicted sequences. The research further highlights its superiority by comparing the CT-Transformer with several state-of-the-art forecasting models. The researchers align the hyperparameters of the involved models, including the proposed model, with those of several baseline models. The research presents the experimental results of the proposed model and the baseline models in Table 3, setting the prediction window to four distinct sizes: 96, 192, 336, and 720. The team conducted three experiments for each size to ensure stable experimental outcomes. The CT-Transformer outperforms the baseline models' overall prediction performance, as demonstrated in the table.