# Novel Data-Driven Models Applied to Short-Term Electric Load Forecasting
###### Abstract
Time-series statistical analysis algorithms (e.g., ARIMA) have not been contemplated as they are trained to specific past values, while our goal is to have a single algorithm that can be trained once and generalizes to new past values. In addition, they are mainly intended for single-output forecasts and their extension to multi-output scenarios (i.e., forecasting \(k\) future values) generates complex models (e.g., VARIMA). To appraise different possible evaluation objectives associated with STLF, we have obtained six different metrics to assess the forecasting performance of the models: mean square error (MSE), mean absolute error (MAE), median absolute error (MAD), coefficient of determination (\(R^{2}\)), relative root mean squared error (RRMSE), and symmetric mean absolute percentage error (sMAPE). We also analyze the influence of the time-ahead forecast interval and the rolling window length on these metrics. Results are presented following three different forecast objectives: very short-term forecasts (immediate time-slots in the forecast time horizon), longer-term forecasts (last time-slots in the forecast time horizon), and forecast average (average of all time-slots in the forecast time horizon). Considering these three scenarios, we have obtained the three best groups of models according to the different forecast objectives: (a) deep learning ensemble models for average results, (b) simple linear regression and Seq2 seq models for very short-term forecasts, and (c) combinations of convolutional/recurrent models and deep learning ensemble models for longer-term forecasts. We have explored the use of deep learning blocks based on the ensemble model presented in [11], called gaNet. The gaNet architecture has been used for IoT traffic prediction [11] and classification [24]. This is the first time that this architecture has been applied to STLF. A gaNet architecture is made up of small deep learning networks formed by a few Convolutional (Conv) and/or RNN layers. These networks are organized as repeating blocks whose outputs are combined (after an aggregation function) into a final output. The input to the architecture is shared by all the blocks. This architecture is connected to gradient boosting models, stacked models [25], and residual networks [26]. It is worth noting the excellent results of the proposed deep learning ensemble model (gaNet) and how it excels in average results and in longer-term (most difficult) forecasts. This good behavior can be connected with having a repeating set of randomly initialized deep learning blocks, in line with other studies that connect the importance of a rich set of random initializations with the behavior of deep learning models [27]. Deep ensembles can also provide an improvement in uncertainty estimates for samples outside the expected data distribution, through appropriate data selection and a specific loss function that maximizes model diversity [28]. This work contributes to provide additional results that confirm the good behavior of deep ensembles under an additional perspective provided by gaNet. In previous works [11; 24], gaNet has been applied to time-series forecasts with a panel data structure (a list of entities, each with an associated time-series), whereas this work applies it to a single time-series with different requirements for data preparation and the validation/testing process. An additional objective of the study is to put forward the availability of accurate forecast results as a valuable tool for identifying new applications, such as: (a) identification of anomalous consumption patterns due to excessive deviations from the forecasts, which can be used as alarms for security or fraud situations and, (b) simulation of what-if non-standard load scenarios and their consequences. These two applications are important for smart grids and their convergence with the IoT (Internet of Things) infrastructure with higher cybersecurity and fraud risks [29; 30].