## 4 Conclusions  
The goal of this study was to develop an energy demand parametric IPIF. Our proposed forecaster predicts energy demand intervals for a 15-min-ahead time horizon and using an \(\alpha\) error rate chosen by the user. The model and its error metrics were computed through a private company's energy demand historical database. The main findings from this study are:  
1. A novel VST parametric IPIF was proposed in order to predict energy demand intervals 15 min ahead. Our forecaster relies on the combination of a PPF to predict energy demand point values, and mathematical concepts as well as t-Student PDF to predict the interval. Concerning the analyzed PPFs, the FFNN model arose as the most suitable one, due to the fact that it has the lowest training and validation RMSE indexes, 0.0853 MW and 0.0766 MW, respectively. 2. The developed IPIF's accuracy was examined for different \(\alpha\) error rates, namely 0.05, 0.10, and 0.15. After performing several analyses, it was concluded that higher error rates generate a decrease in the model's accuracy. However, in our model, this disadvantage can be limited if a sensitivity analysis is done for the \(F\) parameter. In addition, there is a strong relationship between the forecaster's accuracy and prediction interval width, so the knowledge that power systems' decision makers have will allow them to choose if they prefer more accurate or narrower intervals. 3. All of this study's numerical results have been calculated from a private company's energy demand historical database. While the training database contains information about the company's energy demand for 2017, the validation database contains information about the company's 2018 energy demand. A comparison of similar studies in the literature shows that there is a slight improvement when the computed error metrics are examined. The main disadvantage of our proposed model is the fact that at least an entire year's energy demand database was needed to develop the PPF which provides the prediction value. With regard to the proposed interval prediction mathematical model, the main advantage is that even though the model has been fitted for a chosen \(\alpha\) error rate, the user is allowed to compute intervals not only for that \(\alpha\) error rate but also for others. In addition, this study's IPIF model is completely developed through mathematical concepts and t-Student PDF, so our suggested methodology can be applied in other fields where there is desire to predict intervals. Conceptualization, F.R. and J.M.G. ; Formal analysis, A.G.; Investigation, F.R. and N.B. ; Methodology, F.R. and N.B. ; Resources, F.R. and A.G.; Software, F.R. and N.B. ; Supervision, A.G.; Validation, F.R. ; Visualization, J.M.G. ; Writing--original draft, F.R. ; Writing--review & editing, J.M.G. and A.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the Basque Government's Department of Education for financial support through the Researcher Formation Program; grant number PRE_2019\(2\)0035. This research was funded by Fundacion Caja Navarra, Obra Social La Caixa and University of Navarra for financial support through the Mobility Research Formation Program; grant number MOVIL-2019-25. This research was funded by the European Union's Horizon 2020 research and innovation program under grant agreement No 847054. The authors are grateful for the support and contributions from other members of the AmBIENCe project consortium, from VITO (Belgium), ENEA (Italy), TEKNIKER (Spain), INESC TEC (Portugal), ENERGINVEST (Belgium), EDP CNET (Portugal), and BPIE (Belgium). Further information can be found on the project website ([[http://ambience-project.eu/](http://ambience-project.eu/)]([http://ambience-project.eu/](http://ambience-project.eu/)), accessed on 27 May 2020). This research was funded by the ELKARTEK program (CODISAVA KK-2020/00044) of the Basque Government. J.M.G. was supported by VILLUM FONDEN under the VILLUM Investigator Grant (no.