# Addressing the Non-Stationarity and Complexity of Time Series Data for Long-Term Forecasts
## 3 Experiments
### Ablation Study  
To interpret the effects of the individual elements of our model, we observe the performance of our model following the application of several modifications to it. The datasets used in this experiment are ETTm1, ECL, and exchange. For convenient comparison, the batch size and initial learning rates were set to fixed values of 32 and 0.003, respectively, throughout all the experiments. This section can be divided into two sections: the study of the impacts of learning the features in the spectral domain and the usage of \"weak-stationarizing\" and \"non-stationarity restoring\" blocks, and the study of the impact of varying the number of mixer layers.  
4.1 Impact of Processing the Time Series in the Spectral Domain and the Usage of \"Weak-Stationarizing\" and \"Non-Stationarity Restoring\" Blocks  
The observation results for this section can be seen in Table 3. We set up four different variations of our model for this study. The first one is the model suggested in the methodology section without any alteration (results represented by the \"spectral domain\" sub-column under \"with WS and NSR blocks\" column in Table 3). For the second variation, we omit the step of transforming the input into its spectral-domain and instead the output of the \"weak-stationarizing\" block is directly fed to the ConvMixer block for further processing (results represented by the 'time domain' sub-column under \"with WS and NSR blocks\" column in Table 3). The third and fourth variations are to study the effects of the \"weak-stationarizing\" and \"non-stationarity restoring\" blocks, both of which are variations without these blocks. The third variation has a simple skip connection at the same position as the connection between the \"weak-stationarizing\" block and the \"non-stationarity restoring\" block, and the fourth variation does not have this additional skip connection. This third variation is to check whether the effects of the \"weak-stationarizing\" and \"non-stationarity restoring\" blocks are due to the removal and addition of the non-stationary properties or just skip-connection-like properties of the connection between the two blocks.  
The results presented in Table 3 suggest that, except for the instances of ETTm1 with an FHL of 24 and exchange with an FHL of 720, the results of the suggested model are better as compared to the other variations in each instance. While the results of the second and third variations are comparable to that of our model, the fourth variation seems to perform significantly worse. This shows that while the transformation of the input into the spectral  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Model**} & \multicolumn{3}{c}{**With WS and NSR Blocks**} & \multicolumn{3}{c}{**Without WS and NSR Blocks**} \\ \cline{3-10}  & \multicolumn{2}{c}{**Variation’s**} & \multicolumn{2}{c}{**Spectral Domain**} & \multicolumn{2}{c}{**Time Domain**} & \multicolumn{2}{c}{**With Skip Connection**} & \multicolumn{2}{c}{**Without Skip Connection**} \\ \cline{3-10}
**Dataset** & **Metric** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} ETTm1 \\ \end{tabular} } & 24 & 0.253 & 0.313 & 0.256 & 0.314 & **0.232** & **0.300** & 0.260 & 0.330 \\  & 48 & **0.308** & **0.340** & 0.321 & 0.349 & 0.327 & 0.360 & 0.368 & 0.401 \\  & 96 & **0.338** & **0.354** & 0.341 & 0.360 & 0.342 & 0.373 &domain and the transformation of non-stationary input into the weak-stationary form and back via the \"weak-stationarizing\" and \"non-stationarity restoring\" blocks are important, the role of the additional connection between these two blocks is much more noteworthy.