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Section: New Results

Curves classification, denoising and forecasting

Participant : Jean-Michel Poggi.

In collaboration with Anestis Antoniadis (Université J. Fourier, Grenoble) and Irène Gijbels (Leuven Unversity), Jean-Michel Poggi considered a non parametric noisy data model Im1 ${Y_k=f{(x_k)}+\#1013 _k,~k=1,\#8943 ,n,}$ where the unknown signal f from [0, 1] in Im2 $\#119825 $ is assumed to belong to a wide range of function classes, including discontinuous functions and the $ \epsilon$k's are independent identically distributed noises with zero median. The unknown distribution of the noise is assumed to have heavy tails, so that no moments of the noise exist. The design points are assumed to be deterministic points, not necessarily equispaced within the interval [0, 1] . Standard kernel methods cannot be applied in this situation. Their approach first uses local medians to construct variables Zk structured as a Gaussian nonparametric regression, then they apply a wavelet block penalizing procedure adapted to non equidistant designs to construct an estimator of the regression function. Under mild assumptions on the design, they show that their estimator, which has a good practical behavior, simultaneously attains the optimal rate of convergence over a wide range of Besov classes, without prior knowledge of the smoothness of the underlying functions or prior knowledge of the error distribution [3] .

In order to take into account the variation of EDF (the French electrical company) portfolio due to the liberalization of the electrical market, it is essential to conveniently disaggregate the global signal. The idea is to disaggregate the global load curve in such a way that the sum of disaggregated predictions improve significantly the prediction of the global signal considered as a whole. In collaboration with Michel Misiti (Ecole Centrale de Lyon), Yves Misiti (Université Paris-Sud), G. Oppenheim (Université Marne la Vallée), Jean-Michel Poggi designs a strategy to optimize with respect to a predictability index, a preliminary clustering of individual load curves. The optimized clustering scheme is directed by forecasting performance via a cross-prediction dissimilarity index and proceeds as a discrete gradient type algorithm [68] .

- Forecasting time series using wavelets :

Jean-Michel Poggi is the supervisor (with A. Antoniadis) of the PhD Thesis of Jairo Cugliari-Duhalde which takes place in a CIFRE convention with EDF. It is strongly related to the use of wavelets together with curves clustering in order to perform accurate load comsumption forecasting. The thesis develops methodological and applied aspects linked to the electrical context as well as theoretical ones by introducing exogeneous variables in the context of nonparametric forecasting time series.


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