## 5 Experiments
### Parameter Selection Experiments and Results
\(\beta\) regulates the impact of the domain adaptation loss, which is crucial for minimizing the differences in feature distributions across source and target domains, thereby enhancing the model's performance on the target domain. Experiments vary \(\beta\) from 0 to 1 in 0.1 increments, with other parameters held constant. At \(\beta=0\), the model disregards domain adaptation loss, focusing solely on regression losses. With \(\alpha\) set at 0.5 and a 7-day backtracking window, the model forecasts the next day's sales. The results under different domain adaptation loss ratios are detailed in Table 4, with the MAE and RMSE curves compared in Figure 9.  
The analysis of the data and comparison curves from Table 4 and Figure 9 reveals that an initial increase in \(\beta\) from 0 to 0.1 enhances the model performance. However, beyond this point, further increments in \(\beta\) result in performance fluctuations rather than a steady improvement. A \(\beta\) that is too high could cause the model to prioritize reducing domain discrepancies over optimizing the regression task, potentially degrading the overall performance. This suggests that there is a sweet spot for balancing regression loss and domain adaptation loss, which is essential for model tuning. Notably, when \(\beta\) is set to 0.1, the model achieves the best results in forecasting home appliance sales. Consequently, this paper adopts \(\beta\) = 0.1 for all subsequent experiments. The size of the historical backtracking window determines the length of historical information considered by the model when making predictions. Choosing the appropriate window size is crucial for the model to capture long-term dependencies in time series and \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\beta\) & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & **MAPE** \\ \hline
0 & 0.825 & 9.933 & 15.964 & 0.213 \\
0.1 & **0.844** & **9.295** & **15.048** & **0.171** \\
0.2 & 0.827 & 10.124 & 15.866 & 0.200 \\
0.3 & 0.815 & 10.206 & 16.380 & 0.211 \\
0.4 & 0.806 & 10.534 & 16.750 & 0.220 \\
0.5 & 0.814 & 10.329 & 16.441 & 0.212 \\
0.6 & 0.798 & 10.808 & 17.121 & 0.228 \\
0.7 & 0.815 & 10.431 & 16.375 & 0.227 \\
0.8 & 0.807 & 10.679 & 16.737 & 0.227 \\
0.9 & 0.802 & 10.445 & 16.967 & 0.220 \\
1 & 0.807 & 10.497 & 16.763 & 0.223 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results under different ratios of domain adaptation loss. Figure 9: Comparison curves of evaluation metrics under different domain adaptation loss ratios. to improve the predictive performance. To quantitatively analyze the impact of different backtracking window sizes, the size is varied from 4 to 12 days, generating corresponding datasets for training and evaluation. With \(\alpha\) = 0.5 and \(\beta\) = 0.1, the model predicts the sales volume for the next day. The predictive efficacy is evaluated, with the results and comparison curves presented in Table 5 and Figure 10, respectively. The experimental results from Table 5 and Figure 10 indicate that the model's predictive performance follows an increasing and then decreasing trend with the expansion of the historical backtrack window size. Specifically, when the window size is less than 7 days, the model's predictive accuracy improves with the enlargement of the window, likely due to the small window's inability to capture long-term dependencies in the time series, thus limiting its predictive power. However, when the window size exceeds 7 days, the performance begins to decline, possibly because excessive historical information introduces noise and irrelevant data, which reduces its relevance to current sales trends and interferes with the model's prediction of current sales. Additionally, considering the limited number of samples in the target domain of this paper, a larger historical backtrack window could theoretically provide more data but actually lead to a further reduction in available training samples.