## 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
where
the unknown signal f from [0, 1] in is assumed to belong to a
wide range of function classes,
including discontinuous functions and the _{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 Z_{k} 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.