Estimation of a diffusion model with trends taking in account the   extremes. Application to temperature in France
  We built a model of the daily temperature based on a diffusion process and address to extreme values not taken into account in the literature on this kind of models. We first study, using non parametric tools, the trends on mean and variance. In a second step we estimate a stationary model first non parametrically and then using likelihood methods. Extreme values are taken into account in the estimation of model and to obtain a definitive estimation we use in a specific framework extreme theory for diffusions. A test of suitable model by simulation is done. 
Gregory Benmenzer (LJK), Didier Dacunha-Castelle (LM-Orsay), T.T.Huong   Hoang (LM-Orsay)