# Novel Data-Driven Models Applied to Short-Term Electric Load Forecasting
## 4 Results and Discussion
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{Metric} & \multicolumn{1}{c|}{Rank} & \multicolumn{1}{c|}{Gleas} & \multicolumn{1}{c|}{\(\mathbf{f}\)} & \multicolumn{1}{c|}{\(\mathbf{g}\)} & \multicolumn{1}{c|}{\(\mathbf{g}\)} & \multicolumn{1}{c|}{Motel} & \multicolumn{1}{c|}{Metric} \\ \hline \multirow{8}{*}{\(\mathbf{R^{2}}\)} & \multirow{2}{*}{\(1^{\circ}\)} & \multirow{2}{*}{DL Achitectures} & \multirow{2}{*}{1} & \multirow{2}{*}{720} & \multirow{2}{*}{24} & 2 1D-CNN + 1 LSTM & \multirow{2}{*}{0.9087} \\  & & & & & & + 1 FC & \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{2\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type II} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (1 LSTM + 2 FC) \({}^{*}\) 2 + \\  & & & & & & (1 LSTM + 2 FC) \({}^{*}\) 2 + \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{3\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type I} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (3 FC) \({}^{*}\) 5 & 0.9030 \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{1\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type II} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (1 LSTM + 2 FC) \({}^{*}\) 2 + \\  & & & & & (4 FC) \({}^{*}\) 2 & \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{2\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type I} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (4 FC) \({}^{*}\) 5 & 5.7235 \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{3\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type I} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (3 FC) \({}^{*}\) 5 & 5.7410 \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{1\({}^{\circ}\)} & \multirow{2}{*}{DL Achitectures} & \multirow{2}{*}{1} & \multirow{2}{*}{720} & \multirow{2}{*}{24} & 2 1D-CNN + 1 LSTM & \multirow{2}{*}{0.0797} \\  & & & & & & + 1 FC & \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{2\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type II} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (1 LSTM + 2 FC) \({}^{*}\) 2 + \\  & & & & & (4 FC) \({}^{*}\) 2 & & 0.0803 \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{3\({}^{\circ}\)} & \multirow{2}{*}{Ensemble Type I} & \multirow{2}{*}{1} & \multirow{2}{*}{168} & \multirow{2}{*}{24} & (3 FC) \({}^{*}\) 5 & 0.0820 \\ \cline{3-4} \cline{6-8}  & & \multirow{2}{*}{1\({}^{\circ}\)} &  
For near-term forecasts (prediction of the following value), the linear/simple models, as linear regression, provide the best results when using a large enough number of predictors (\(p=128\)) and a simple scalar predictor value (\(f=1\)), which is the electric load. In this scenario, another model providing the best results is the Seq2 seq+attention model with a smaller number of predictors (\(p=24\)) and the full vector of predictor values (\(f=45\)). * For longer-term forecasts, the deep learning models with one or two LSTM layers provide the best results. Another model with excellent performance is a model combining 1D-CNN layers and LSTM layers. The model with the best stMAPE metric is an ensemble Type II model with a small number of dense and LSTM blocks. In all these cases, the best results are obtained with a large number of predictors (\(p=168\), \(720\)) and a smaller number of values per predictor (\(f=1\)). * Considering the average results for the 24 predicted values, the best results are obtained for: (1) ensemble Type II models with a small number of dense and LSTM blocks, (2) ensemble Type I models with a small number of dense blocks, and (3) combined 1D-CNN and LSTM layers with \(p=720\). All these results are obtained with the smaller number of values per predictor (\(f=1\)). * Interestingly, multiple output models can produce better results for distant forecasts than single output models (classic ML models) even when the latter models have a specific regressor to predict each output. This is a demonstration of the great correlation between the outputs that a single model can learn, while \(k\) independent regressors lose this valuable information.