Estimation of a diffusion model with trends taking into account the extremes. Application to temperature in France



We built a model for daily temperatures based on a seasonal functional heteroscedastic autoregressive model (SFHAR) and address also to extremes values, not taken in account in the literature concerning these topics. Reduced series are obtained after removing the trend and seasonality components by both nonparametric and parametric methods. Then, we model the reduced series by a periodic-stationary (cycloperiodic) model. The seasonality remains in all the dynamics of reduced series and is important. On the other hand, we use the specific framework extreme theory for bounded diffusions corresponding to Weibull case to obtain the final estimate. The model is tested by simulations. Copyright © 2011 John Wiley & Sons, Ltd.