Forecasting intra day load curves using sparse functional regression

Abstract

In this paper we provide a prediction method, the prediction box, based on a sparse learning process elaborated on very high dimensional information, which will be able to include new - potentially high dimensional - influential variables and adapt to different contexts of prediction. We elaborate and test this method in the setting of predicting the national French intra day load curve, over a period of time of 7 years on a large data basis including daily French electrical consumptions as well as many meteorological inputs, calendar statements and functional dictionaries. The prediction box incorporates a huge contextual information coming from the past, organizes it in a manageable way through the construction of a smart encyclopedia of scenarios, provides experts elaborating strategies of prediction by comparing the day at hand to referring scenarios extracted from the encyclopedia, and then harmonizes the different experts. More precisely, the prediction box is built using successive learning procedures: elaboration of a data base of historical scenarios organized on a high dimensional and functional learning of the intra day load curves, construction of expert forecasters using a retrieval information task among the scenarios, final aggregation of the experts. The results on the national French intra day load curves strongly show the benefits of using a sparse functional model to forecast the electricity consumption. They also appear to meet quite well with the business knowledge of consumption forecasters and even shed new lights on the domain.