## 5 Experiments
### Comparative Experiments and Results
This may be due to challenges in capturing long-term dependencies in time series data and susceptibility to the vanishing gradient problem. CNN exhibits a relatively stable performance across various forecast steps but falls short of the combined models in overall predictive accuracy, indicating that convolutional operations alone may not be sufficient to fully explore the temporal characteristics of time series data. Combined models like CNN-LSTM and CNN-LSTM-Attention achieve superior predictive performance, with CNN-LSTM-Attention showing a high R\({}^{2}\) value (0.797) at a 1-day step and maintaining a relatively stable performance even at a 4-day step. This indicates that integrating convolutional operations with LSTM or attention mechanisms can better model time series data, capturing both local and global features, thereby enhancing the predictive accuracy. The TransCNN-LSTM-Attention model, which incorporates TL, demonstrates exceptional performance in both short-term and long-term forecasting tasks, outperforming CNN-LSTM-Attention in most evaluation metrics and forecast horizons and ranking just below the TransTLA model overall. This shows that TL can further enhance sales forecasting performance by leveraging knowledge from related domains. Notably, the TransTLA model proposed in this paper exhibits the best overall predictive performance across all forecast horizons. Table 9 presents the percentage MAE improvement of the TransTLA model over some comparative models. When predicting 1-day sales, its MAE is reduced by 9.83% compared to the CNN-LSTM-Attention model and by 9.29% compared to the second-best TransCNN-LSTM-Attention model. Especially in multi-step forecasting, its evaluation metrics are better than other comparative models. For instance, at a 3-day forecast step, the MAE is reduced by 12.12% compared to the CNN-LSTM-Attention model and by 10.53% compared to the TransCNN-LSTM-Attention model. This indicates that the components of the TransTLA model, such as TCN and TL, can more effectively mine intrinsic patterns and trends from time series data, further validating its high efficiency and robustness in multi-step forecasting tasks. In addition to the superior predictive performance, it is also crucial to consider the computational complexity of these models. Table 10 presents the number of floating-point operations (FLOPs), multiply-accumulate operations (MACs), and parameters (Params) for different models used in the experiments, based on the settings described in Section 5.3. From Table 10, we can observe that the TransTLA model has higher FLOPs and MACs compared to most other models, indicating greater computational complexity. However, this complexity is justified by its significantly improved predictive performance. When comparing with simpler models like ARIMA, XGBoost, and SVR, the complexity of DL models including TransTLA is considerably higher. Traditional models such as ARIMA and SVR generally have lower computational complexity due to their simpler structure and fewer parameters. XGBoost, while more complex than ARIMA and SVR, still does not reach the level of complexity seen in DL models. However, these traditional models often fall short in capturing the intricate patterns and dependencies in time series data, especially for multi-step forecasting tasks, where the TransTLA model excels. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Compared Model** & **Step Size 1** & **Step Size 2** & **Step Size 3** & **Step Size 4** & **Average** \\ \hline CNN & 11.06 & 8.34 & 12.31 & 5.19 & 9.23 \\ CNN-LSTM & 11.94 & 9.18 & 11.11 & 3.66 & 8.97 \\ CNN-LSTM-Attention & 9.83 & 13.34 & 12.12 & 8.72 & 11.00 \\ TransCNN-LSTM-Attention & 9.29 & 7.99 & 10.53 & 6.14 & 8.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The MAE performance improvement of the TransTLA model over comparative models (percentage). It is worth noting that the addition of TL in models leads to the number of parameters remaining unchanged, but the computational cost actually doubles.