# Prediction Interval Adjustment for Load-Forecasting using Machine Learning
## 4 Experiments and Results
### Results and Discussion
Also, probabilistic RMSE shows that the probabilistic error tends to be larger than MAE along the horizons, but the maximum difference between Adjusted and Normal probabilistic RMSE is less than 6 MW, which is also not significant. This significance is measured by the ancillary services requirements [35]. Ancillary services requirements are published daily in the Independent System Operator official site. For the region this method is applied, the requirements of the ancillary services for the first horizon is a constant value of 25 MW. This means that errors below 25 MW do not affect the power systems significantly. Also, it is worth mentioning that probabilistic MAE and RMSE are smaller in the Weekend experiment. This behavior may happen point-forecast RMSE and MAE are larger in the Weekend experiment, so we can expect prediction intervals to be larger on  
Figure 14: Probabilistic MAE (Means Absolute Error) and RMSE (Root Mean Squared Error) for (from **top** to **bottom**) the persistence, ARIMA (Autoregressive Integrated Moving Average) and the proposed model. Weekends. In general, we can observe that the error metrics of the Adjusted prediction intervals are similar to the Normal prediction intervals. To understand better this similarity, we make use of PICP per period. In Figure 15 the PICP per period for all the three experiments and the three models is shown. As we can observe in Figure 15, for the ARIMA and the persistence models, Normal and Adjusted PIPC are similar. However, we can also observe that RMSE and MAE are larger than the measured for the proposed approach. Also, it is interesting to observe that ARIMA and persistence models have larger errors in the periods of 08:00-12:00 and 15:45-19:00, this may be caused by the load change during the day with respect to the sun position. Also, it is interesting to observe that these errors are lower in the persistence model for the periods 15:45-19:00. For the proposed approach, we can observe that probabilistic MAE and RMSE are more stables along the periods than the measured of the ARIMA and the persistence model. Also, we can observe that although Adjusted PICP drops until less than 75%, probabilistic MAE indicates that the error is always less than 5 MW, which is not significant. Also, probabilistic RMSE shows that in most of the periods the error is less than 15 MW, which is also not significant. A prediction interval creation method is presented. The proposed approach for the creation of the prediction interval allows modifying the prediction interval by means of an association rules method. Using the proposed approach, the prediction interval can be reduced as much as the corresponding support value. We construct prediction intervals using Artificial Neural Network models and we adjust them by means of rules obtained with the _a priori_ algorithm. Prediction interval quality and effectiveness are measured by means of Prediction Interval Coverage Probability (PICP) and the Dawid-Sebastiani Score (DSS). PICP and DSS per horizon show that the Adjusted and Normal prediction intervals are pretty similar. The proposed approach was compared to the ARIMA model and a persistence model. The proposed model demonstrates to have better performance in all the prediction interval evaluation metrics. Also, probabilistic and point-forecast MAE and RMSE metrics are used. Probabilistic MAE indicates that Adjusted prediction intervals fail by less than 2.5 MW along  
Figure 15: PICP comparison of Normal vs Adjusted prediction intervals, and probabilistic MAE/RMSE for the Adjusted prediction intervals per period. the horizons, which is not significant if we compare it to the 1.3 MW the Normal prediction interval failure. Also, probabilistic RMSE shows that the probabilistic error tends to be larger than MAE along the horizons, but the maximum difference between Adjusted and Normal probabilistic RMSE is less than 6 MW, which is also not significant.