Mathilde Mougeot (Université Paris Diderot)

An important perspective in electric consumption is the forecasting and then it is crucial to establish a modeling process relying on a small number of appropriated predictors, in such a way that the prediction shows robustness and efficiency qualities. In our context, it is commonly admitted that a large set of potential predictors among climate variables and shape ’patterns’ are influential for the prediction implying high dimensional models associated with correlated covariates. We use a model and then a forecasting of the intraday load curve, based on a high dimensional regression model. The intraday signal denoted by Y is sampled half-hourly on 24 hours. In a functional regression setting we put Y = f(x) + eps and assume that the function f can be described by a linear combination of a small number (S) of functions belonging to a dictionary D = (fg1;..; gpg, plus a small correction term. To estimate the coefficient of the regression, we use the LOL (Learning Out of Leaders) algorithm. This algorithm is based on a two steps thresholding procedure especially suitable for very high dimensional models, p > n. To fit the electrical consumption many dictionaries can be used such as for instance combinations of bases (Fourier bases, Haar bases, wavelet bases...) or exogeneous functions reflecting the climate variables. We provide in this talk a forecasting model for the intraday load curve, using several prediction models provided by different ’experts’. Each expert provides a model based on a strategy for choosing the most accurate selection of dictionary variables and estimation of the linear combination. The final prediction is obtained using an aggregation of these different forecasters, with exponential weights. In the forecasting perspective, the sparse model appears then as crucial, since based on only a few coefficients, it allows fitting and forecasting very promising results. We present here in details, the different dictionaries, models experts and forecasting performances.