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

TL;DR

This paper develops a diffusion-based model for daily temperature in France that incorporates extreme values, using non-parametric and likelihood methods, and applies extreme value theory for improved estimation and model validation.

Contribution

It introduces a novel approach to modeling temperature with diffusion processes that explicitly accounts for extremes, enhancing existing temperature modeling techniques.

Findings

Model effectively captures temperature trends and extremes.

Likelihood estimation improves parameter accuracy.

Simulation tests validate model suitability.

Abstract

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.