## 4 Experiments Analysis and Discussion
### Comparison with Other Frontier Methods  
TSNN-ESTD utilizes the short-term forecast to mitigate the long-term forecast with the ensemble strategy, which enriches the capability of long-term dependency capturing. Tables 2 and 3 demonstrates the performance of TSNN-ESTD and other frontier methods on four benchmark datasets and one composite dataset. The prediction time step is set to 96 with reference to the current literature. \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset** & **Variates** & **Time Steps** & **Granularity** \\ \hline ECL & 321 & 26,305 & 1 h \\ Exchange & 8 & 7588 & 1 day \\ Traffic & 862 & 17,544 & 1 h \\ Weather & 21 & 52,696 & 10 min \\ ETT & 7 & 17,420/69,680 & 1 h/15 min \\ ERA5 & 38 & 17,544 & 1 h \\ \hline \end{tabular}
\end{table} 
Table 1: Data statistics. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{2}{c}{**ECL**} & \multicolumn{2}{c}{**Exchange**} & \multicolumn{2}{c}{**Traffic**} & \multicolumn{2}{c}{**Weather**} \\ \hline  & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline iTransformer [28] & 0.148 & 0.240 & 0.086 & 0.206 & 0.395 & 0.268 & 0.174 & 0.214 \\ Rlinear [18] & 0.201 & 0.281 & 0.093 & 0.217 & 0.649 & 0.389 & 0.192 & 0.232 \\ Dlinear [19] & 0.197 & 0.282 & 0.088 & 0.218 & 0.650 & 0.396 & 0.196 & 0.255 \\ PatchTST [29] & 0.181 & 0.270 & 0.088 & 0.205 & 0.462 & 0.295 & 0.177 & 0.218 \\ Crossformer [30] & 0.219 & 0.314 & 0.256 & 0.367 & 0.522 & 0.290 & 0.158 & 0.230 \\ TiDE [31] & 0.237 & 0.329 & 0.094 & 0.218 & 0.805 & 0.493 & 0.202 & 0.261 \\ TimesNet [32] & 0.168 & 0.272 & 0.107 & 0.234 & 0.593 & 0.321 & 0.172 & 0.220 \\ SCINet [33] & 0.247 & 0.345 & 0.267 & 0.396 & 0.788 & 0.499 & 0.221 & 0.306 \\ FEDformer [34] & 0.193 & 0.308 & 0.148 & 0.278 & 0.587 & 0.366 & 0.217 & 0.296 \\ Stationary [35] & 0.169 & 0.273 & 0.111 & 0.237 & 0.612 & 0.338 & 0.173 & 0.223 \\ Autoformer [36] & 0.201 & 0.317 & 0.197 & 0.323 & 0.613 & 0.388 & 0.266 & 0.336 \\ \hline TSNN-ESTD & 0.133 & 0.225 & 0.046 & 0.152 & 0.585 & 0.427 & 0.129 & 0.151 \\ \hline \end{tabular}
\end{table} 
Table 2: Performance on four benchmark datasets. Rlinear [18] employs a linear transformation approach for time-series forecasting, demonstrating that simple linear models can effectively capture complex temporal patterns. Dlinear [19] employs a deep linear model for time-series forecasting, demonstrating that deep linear architectures can effectively capture temporal patterns. iTransformer reimagines transformer architecture for time-series forecasting by embedding each time series as variate tokens, enabling the capture of multivariate correlations through self-attention mechanisms. PatchTST [29] treats time-series data as sequences of patches, similar to image processing, allowing the transformer to model long-term dependencies effectively. Crossformer [30] introduces a cross-dimensional attention mechanism to capture both temporal and inter-variable dependencies in multivariate time-series forecasting. TiDE [31] focuses on modeling temporal dynamics by decomposing time series into trend and seasonal components, enhancing forecasting accuracy. TimesNet [32] utilizes a temporal 2D-variation modeling approach to capture complex temporal patterns in time-series data. SCINet [33] introduces a sample convolutional interaction network to model complex temporal dynamics in time-series forecasting. FEDformer [34] enhances transformer models by incorporating frequency decomposition, allowing the model to capture both short-term and long-term dependencies in time-series data. Stationary [35] focuses on modeling non-stationary time-series data by introducing a stationarity assumption, improving forecasting performance. Autoformer [36] introduces an auto-correlation mechanism to transformer models, enabling the capture of both trend and seasonal components in time-series forecasting.