## 3 Price Predictions Using Deep Learning Models
### Training Prediction Models  
To determine the most suitable forecasting model for the system, we evaluated Naive Seasonal Prediction, GRU, LSTM, N-BEATS, and N-HiTS models in various configurations on randomly selected days throughout 2023. Given the inherent variability in the market data, it is unrealistic to expect a single model to consistently perform best every day. However, in the initial testing phase, N-HiTS demonstrated superior overall performance during both training and validation, making it the primary model chosen for the proposed system. We trained N-HiTS models on the target dataset using the hyperparameters and details indicated in Table 1.  
To demonstrate both the efficacy of the N-HiTS architecture and the proposed system as a whole, we adopted a seasonal cross-validation approach. Four representative months were randomly chosen for each season in the year 2023, resulting in the selection of February (winter), April (spring), July (summer), and October (autumn). Predictions were generated for the 15 th day of each chosen month, utilizing the preceding 365 days' worth of hourly data for model training. Subsequently, the trained model was leveraged to predict the next 24 h, relying on the past week's data as input. A performance comparison of the predictions was conducted using established metrics, with the predicted data additionally employed in an SLB storage system as a proof-of-concept demonstration. Our results demonstrate that N-HiTS is superior in most scenarios, but it is still profitable when it is not the best model. To evaluate the findings, we used some common metrics such as the Mean Absolute Error (MAE) (1), Mean Squared Error (MSE) (2), Root Mean Squared Error (RMSE) (3), Coefficient of Variation (COEV) (4), Mean Absolute Percentage Error (MAPE) (5), and Mean Directional Accuracy (MDA) (6). The MAE quantifies the average magnitude of errors between predicted values and actual observations, providing a straightforward indication of forecasting accuracy. It is calculated by averaging the absolute differences between predicted and observed values. However, the MAE does not account for the direction of errors, treating both underestimations and overestimations equally. In contrast, the MSE squares the errors before averaging them, offering a more sensitive measure by penalizing larger discrepancies. This property makes the MSE particularly useful for identifying outliers and amplifying the impact of large errors on the overall assessment of model performance. The RMSE, a derivative of the MSE, shares its benefits while addressing the issue of scale inherent in the MSE. By taking the square root of the MSE, the RMSE yields a metric that is interpretable in the same units as the original data, facilitating a more intuitive understanding of prediction accuracy. The COEV offers a normalized assessment of forecasting accuracy by considering the variability relative to the mean of the observed data. The MAPE provides a percentage-based evaluation of forecasting performance, making it highly interpretable and widely favored in practical applications. The MAPE computes the average of the absolute percentage errors between predicted and observed values, offering insights into the relative accuracy of predictions across different scales of the time-series data. The MDA compares the forecast direction (increments or decrements in value) to the actual realized direction. It should be noted that the MDA does not directly reflect the accuracy of the forecast but demonstrates how accurately a model can predict changes in the directions that might affect the system's decision-making process. Metrics are calculated using the Equations (1)-(5), where N denotes the number of data points in the test data. \(y_{t}\) denotes the actual value and \(\hat{y}\) denotes the predicted value. \(\overline{y_{t}}\) is the average of \(y_{t}\).