# Time Series Forecasting Method Based on Multi-Scale Feature Fusion and Autoformer
## 3 Results
### Method Validation on Diverse Data
#### 3.3.1 Prediction Experiments in the Disease Field  
In real life, the spread of infectious diseases and apparel sales are both closely related to seasonal changes. Their time-series data features are affected by seasonal and trending factors, showing certain patterns. Therefore, we give priority to the disease-related dataset for testing. In the disease field, we chose the Illness (ILI) dataset for time-series prediction. The ILI dataset contains weekly records of influenza-like illness (ILI) patients from the US Centers for Disease Control and Prevention during 2002-2021, reflecting the proportion of ILI patients among all patients. On the ILI dataset, the MD-Autoformer model shows superior predictive performance. As shown in Table 4, MD-Autoformer has lower RMSE and MAE values than other models at different prediction steps. For instance, at 24-step prediction, MD-Autoformer's RMSE is 1.385 and the MAE is 0.834, compared to 1.866, 2.401, 2.098, and 1.489 for RMSE, and 1.287, 1.677, 1.382, and 1.084 for the MAE of Autoformer, Informer, and DLinear, respectively. This indicates that the MD-Autoformer can capture the periodicity and trending characteristics of disease data more accurately. Moreover, the MD-Autoformer has smaller standard deviations at different prediction steps, showing higher stability. For example, at 60-step prediction, its RMSE standard deviation is \(\pm\)0.039, and the MAE standard deviation is \(\pm\)0.015. A low standard deviation indicates that MD-Autoformer maintains a stable level of precision in repeated experiments. As shown in Figure 5, MD-Autoformer, Autoformer, and DLinear all effectively capture the upward and downward trends in disease data, with their changing trends being consistent with the true values at multiple peaks or troughs. Although DLinear has slightly higher RMSE and MAE than MD-Autoformer, its ability to capture sequence trends is commendable. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Methods**} & \multicolumn{2}{c}{**MD–Autoformer**} & \multicolumn{2}{c}{**Autoformer**} & \multicolumn{2}{c}{**Informer**} & \multicolumn{2}{c}{**Reformer**} & \multicolumn{2}{c}{**DLinear**} \\ \hline \multicolumn{1}{c}{**Metric**} & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline \multirow{4}{*}{ILI} & 24 & 1.385 \(\pm\) 0.022 & 0.834 \(\pm\) 0.014 & 1.866 & 1.287 & 2.401 & 1.677 & 2.098 & 1.382 & 1.489 & 1.084 \\  & 36 & 1.296 \(\pm\) 0.023 & 0.736 \(\pm\) 0.013 & 1.762 & 1.148 & 2.181 & 1.467 & 2.187 & 1.448 & 1.462 & 1.018 \\  & 48 & 1.318 \(\pm\) 0.062 & 0.777 \(\pm\) 0.018 & 1.634 & 1.085 & 2.182 & 1.469 & 2.198 & 1.465 & 1.460 & 1.031 \\  & 60 & 1.357 \(\pm\) 0.039 & 0.813 \(\pm\) 0.015 & 1.664 & 1.125 & 2.294 & 1.564 & 2.210 & 1.483 & 1.540 & 1.098 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results of different models on ILI dataset. To further validate the capability of MD-Autoformer in high-frequency financial time series forecasting tasks, we collected data from QQQ, an ETF managed by Invesco Ltd. (Atlanta, GA, USA) that tracks the NASDAQ-100 Index. The dataset spans from 10 March 1999 to 10 November 2017 and includes daily metrics such as open, close, high, and low prices, and trading volume. We conducted comparative experiments targeting the prediction of closing prices over a 60-day horizon. During the experiments, the lookback window lengths of baseline models were allowed to vary. This design accounts for the observation that Transformer-based models tend to overfit with extended lookback windows, while DLinear exhibits underfitting tendencies. Consequently, the lookback  
As shown in Table 6, compared with Autoformer, MD-Autoformer reduces RMSE by 10.41% and MAE by 6.29%, indicating a marked rise in forecasting accuracy. DLinear and Autoformer also show low RMSE and MAE, meaning their prediction values are close to the true values. Figure 7 reveals that MD-Autoformer and DLinear have trends closer to the true values.