Evaluation and validation of forecasts in law.

Summary This thesis deals with the evaluation and validation of law forecasts. In the first part, we are interested in the contribution of machine learning to quantile and law predictions. To do so, we have tested different machine learning algorithms in a framework of quantile forecasts on real data. We thus try to highlight the interest of certain methods according to the type of data we are confronted with. In the second part, we present some validation tests of law predictions present in the literature. Some of these tests are then applied on real data related to the log-returns of stock market indices. In the third part, we propose a recalibration method allowing to simplify the choice of a particular density forecast compared to others. This recalibration allows us to obtain valid forecasts from a misspecified model. We also highlight conditions under which the quality of recalibrated forecasts, as assessed using CRPS, is systematically improved, or very slightly degraded. These results are illustrated through applications to temperature and price scenarios.