# Time Series Forecasting Method Based on Multi-Scale Feature Fusion and Autoformer
## 3 Results
### Clothing Sales Forecasting: Case Study  
To evaluate the effectiveness of the proposed method on the apparel sales forecasting task, we conducted a comparative experiment between the proposed method and Autoformer, Informer [30], Reformer [31], and DLinear [32] on a real apparel sales forecasting task, and the experimental results are shown in Table 2.  
The experiments were conducted independently multiple times, and the average values were taken to minimize the potential interference of random factors on the model evaluation results. The experimental results show that our proposed method outperforms other classical methods in most cases. Specifically, at 24-step forecasting, our method achieves a RMSE of 2.165 and an MAE of 0.761, which are significantly lower than the other models compared, and have higher forecasting accuracy. From the trend analysis of errors, compared to Autoformer, when the prediction step size is 24, MD-Autoformer achieved a 24.47% reduction in RMSE and a 39.33% reduction in MAE; when the prediction step size increased to 60, the RMSE decreased by 22.36%, and the MAE decreased by 24.93%. DLinear also performs well. In the experiment with a prediction length of 60, DLinear's RMSE is 2.852 and MAE is 1.146, which is more accurate than Autoformer's prediction. This indicates that MD-Autoformer has a significant advantage in short-term apparel sales forecasting, particularly excelling in reducing the mean absolute error. Due to the lack of ability to extract time series information for different scales with seasonal trend prediction, the experimental errors demonstrated by Informer and Reformer gradually expand with increasing prediction steps, while our method has a lower growth rate of errors in 36, 48, and 60-step prediction, which further verifies that multi-scale feature fusion networks with date-time coding can effectively extract the hidden information of time series of different lengths, which overall improves the prediction performance for long-time apparel sales tasks. In the Apparel Sales forecasting experiment, we focus not only on the prediction accuracy of the model but also on its stability and reliability. For this purpose, we have conducted a standard deviation analysis of the experimental results of each model. As shown in Table 3, the MD-Autoformer model has relatively small standard deviations in RMSE and MAE across different prediction steps. This indicates that the model performs consistently in multiple experiments with little fluctuation in prediction errors. In contrast, other models like Informer and Reformer have larger standard deviations, meaning their prediction results vary more significantly across different experiments, making them less stable. In summary, the MD-Autoformer model not only excels in prediction accuracy but also demonstrates a clear advantage in stability. This makes the model more reliable for practical applications, providing stable decision-making support for tasks like apparel sales forecasting. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Methods**} & \multicolumn{2}{c}{**MD–Autoformer**} & \multicolumn{2}{c}{**Autoformer**} & \multicolumn{2}{c}{**Informer**} & \multicolumn{2}{c}{**Reformer**} & \multicolumn{2}{c}{**DLinear**} \\ \hline
**Metric** & & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline \multirow{4}{*}{Apparel Sales} & 24 & 2.165 & 0.761 & 2.851 & 1.256 & 2.865 & 1.286 & 3.595 & 2.077 & 2.669 & 1.004 \\  & 36 & 2.257 & 0.847 & 2.879 & 1.158 & 2.898 & 1.334 & 3.824 & 2.076 & 2.746 & 1.034 \\  & 48 & 2.320 & 0.876 & 2.949 & 1.199 & 2.981 & 1.391 & 4.274 & 2.251 & 2.838 & 1.083 \\  & 60 & 2.270 & 0.893 & 2.912 & 1.191 & 2.985 & 1.436 & 4.504 & 2.399 & 2.852 & 1.146 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative experimental results for different prediction step sizes on Apparel Sales.