# Temporal Convolutional Networks Applied to Energy-Related Time Series Forecasting
## 3 Results and Discussion
### Forecasting Accuracy
\begin{table}
\begin{tabular}{c c|c c c c c c c|c} \hline \multicolumn{1}{c|}{**Past History**} & \multicolumn{1}{c|}{**Model Description**} & \multirow{2}{*}{**WAPE**} \\ \cline{3-3} \cline{5-10}
**Time-Steps** & & \# & **Type** & **Blocks** & **Filters** & **Kernel** & **Dilations** & **Batch Size** & **Epochs** \\ \hline \multirow{2}{*}{144} & \multirow{2}{*}{24} & 1 & LSTM & 3 & 128 & & & 128 & 50 & 0.0105 \\  & & 2 & TCN & 2 & 128 & 6 & [1, 3, 6, 12] & 256 & 50 & 0.0104 \\ \hline \multirow{2}{*}{168} & \multirow{2}{*}{28} & 3 & LSTM & 3 & 128 & & & 128 & 50 & 0.0109 \\  & & 7 & TCN & 2 & 128 & 6 & [1, 5, 7, 14] & 128 & 50 & 0.0096 \\ \hline \multirow{2}{*}{288} & \multirow{2}{*}{48} & 5 & LSTM & 3 & 128 & & & 128 & 50 & 0.0151 \\  & & 6 & TCN & 2 & 128 & 6 & [1, 3, 6, 12, 24] & 128 & 50 & **0.0093** \\ \hline \multicolumn{10}{c}{**b** Best results for the EV power consumption data.} \\ \hline \multicolumn{10}{c}{**Past History**} & \multicolumn{1}{c|}{**Model Description**} & \multirow{2}{*}{**WAPE**} \\ \cline{3-3} \cline{5-10}
**Time-Steps** & & \# & **Type** & **Blocks** & **Filters** & **Kernel** & **Dilations** & **Batch Size** & **Epochs** \\ \hline \multirow{2}{*}{168} & \multirow{2}{*}{7} & 7 & LSTM & 2 & 128 & & 128 & 50 & 0.4317 \\  & & 8 & TCN & 1 & 128 & 3 & [1, 5, 7, 14, 28, 56] & 128 & 50 & 0.4272 \\ \hline \multirow{2}{*}{336} & \multirow{2}{*}{14} & 9 & LSTM & 3 & 64 & & 64 & 50 & 0.4429 \\  & & 10 & TCN & 2 & 128 & 3 & [1, 5, 7, 14, 28, 56] & 64 & 100 & **0.4228** \\ \hline \multirow{2}{*}{672} & \multirow{2}{*}{28} & 11 & LSTM & 2 & 64 & & 64 & 50 & 0.4336 \\  & & 12 & TCN & 2 & 64 & 6 & [1, 5, 7, 14, 28, 56] & 64 & 50 & 0.4319 \\ \hline \end{tabular}
\end{table} 
Table 3: WAPE results of the best TCN and Long Short-Term Memory (LSTM) models for each possible value of input window. Figure 6: Distribution of weighted absolute percentage error (WAPE) results for all architectures depending on the past history window. 14, 28, and 56. This model has been trained over 100 epochs with a batch size of 64 instances. Similar to the previous dataset, the best LSTM model (0.04317 WAPE) uses the smallest possible input window, which is 7 days. This LSTM model consists of 2 stacked layers with 128 units and was trained over 50 epochs using 128 as batch size. Given the different nature of this dataset, the best configurations of architectures present several differences. For TCNs, a smaller kernel was able to extract the underlying patterns more accurately. Furthermore, a smaller batch size was better in almost all cases since the EV time series has fewer instances to train with. In addition, Figure 8 shows the evolution of the training and validation loss for the best TCN and LSTM models. These plots can help to compare the learning process of the different architectures presented in Table 3. It can be seen that TCNs have a more stable loss optimisation procedure compared to the LSTM models, which can be associated with the use of the standard backpropagation method. The training curves of convolutional networks suffer fewer oscillations than the recurrent approach. For the electric demand dataset, TCN models converge faster to a lower validation loss. However, for the EV power demand data, LSTMs have an inferior validation loss at the initialisation point and hence converge more rapidly. In general, the obtained results demonstrate that TCN models can outperform the forecasting accuracy of LSTM models. TCNs have shown a more reliable performance regardless of the selected architecture and parametrisation. The dilated casual convolutions employed by TCNs were better at capturing long-term dependencies than recurrent units. Other important conclusions can be drawn  
Figure 7: Architecture of the best TCN model for each dataset. from the experimental results of this study. As can be seen, the best LSTM models for both datasets use the smallest possible input window. This indicates that the sequential processing of recurrent networks is not optimal for dealing with very long input sequences.