Nonlinear models and forecasting.

Summary The interest of non-linear models lies, on the one hand, in a better consideration of the non-linearities characterizing macroeconomic and financial series and, on the other hand, in a more information-rich forecast.At this level, the originality of the intervals (asymmetric and/or discontinuous) and the forecasting densities (asymmetric and/or multimodal) offered by this new form of modelling suggests that an improvement in forecasting relative to linear models is possible, and that sufficiently powerful evaluation tests are needed to verify this possible improvement. These tests generally consist in checking distributional hypotheses on the violation processes and the probabilistic transforms associated with each of these forms of forecasting. In this thesis, we have adapted the GMM framework based on orthonormal polynomials designed byBontemps and Meddahi (2005, 2012) to test the fit to certain probability laws, an approach already initiated by Candelon et al. (2011) in the context of Value-at-Risk assessment. In addition to the simplicity and robustness of the method, the tests developed have good properties in terms of size and power. The use of our new approach in the comparison of linear and non-linear models in an empirical analysis confirmed the idea that the former are preferred if the objective is the calculation of simple point forecasts while the latter are the most appropriate to account for the uncertainty around them.