L’intérêt des modèles non-linéaires réside, d’une part, dans une meilleure prise en compte des non-linéaritéscaractérisant les séries macroéconomiques et financières et, d’autre part, dans une prévision plus riche en information.A ce niveau, l’originalité des intervalles (asymétriques et/ou discontinus) et des densités de prévision (asymétriqueset/ou multimodales) offerts par cette nouvelle forme de modélisation suggère qu’une amélioration de la prévisionrelativement aux modèles linéaires est alors possible et qu’il faut disposer de tests d’évaluation assez puissants pourvérifier cette éventuelle amélioration. Ces tests reviennent généralement à vérifier des hypothèses distributionnellessur les processus des violations et des transformées probabilistes associés respectivement à chacune de ces formes deprévision. Dans cette thèse, nous avons adapté le cadre GMM fondé sur les polynômes orthonormaux conçu parBontemps et Meddahi (2005, 2012) pour tester l’adéquation à certaines lois de probabilité, une approche déjà initiéepar Candelon et al. (2011) dans le cadre de l’évaluation de la Value-at-Risk. Outre la simplicité et la robustesse de laméthode, les tests développés présentent de bonnes propriétés en termes de tailles et de puissances. L’utilisation denotre nouvelle approche dans la comparaison de modèles linéaires et de modèles non-linéaires lors d’une analyseempirique a confirmé l’idée selon laquelle les premiers sont préférés si l’objectif est le calcul de simples prévisionsponctuelles tandis que les derniers sont les plus appropriés pour rendre compte de l'incertitude autour de celles-ci. / The interest of non-linear models is, on the one hand, to better take into account non-linearities characterizing themacroeconomic and financial series and, on the other hand, to get richer information in forecast. At this level,originality intervals (asymmetric and / or discontinuous) and forecasts densities (asymmetric and / or multimodal)offered by this new modelling form suggests that improving forecasts according to linear models is possible and thatwe should have enough powerful tests of evaluation to check this possible improvement. Such tests usually meanchecking distributional assumptions on violations and probability integral transform processes respectively associatedto each of these forms of forecast. In this thesis, we have adapted the GMM framework based on orthonormalpolynomials designed by Bontemps and Meddahi (2005, 2012) to test for some probability distributions, an approachalready adopted by Candelon et al. (2011) in the context of backtesting Value-at-Risk. In addition to the simplicity androbustness of the method, the tests we have developed have good properties in terms of size and power. The use of ournew approach in comparison of linear and non-linear models in an empirical analysis confirmed the idea according towhich the former are preferred if the goal is the calculation of simple point forecasts while the latter are moreappropriated to report the uncertainty around them.

The primary objective of this dissertation is to revisit the CAPM and the Fama-French multi-factor models with a view to evaluate the validity of the probabilistic assumptions imposed (directly or indirectly) on the particular data used. By thoroughly testing the assumptions underlying these models, several departures are found and the original linear regression models are respecified. The respecification results in a family of heterogeneous Student's t models which are shown to account for all the statistical regularities in the data. This family of models provides an appropriate basis for revisiting the empirical adequacy of the CAPM and the Fama-French multi-factor models, as well as other models, such as alternative asset pricing models and risk evaluation models. Along the lines of providing a sound basis for reliable inference, the respecified models can serve as a coherent basis for selecting the relevant factors from the set of possible ones. The latter contributes to the enhancement of the substantive adequacy of the CAPM and the multi-factor models. / Ph. D. / The primary objective of this dissertation is to revisit the CAPM and the FamaFrench multi-factor models with a view to evaluate the validity of the probabilistic assumptions imposed (directly or indirectly) on the particular data used. By probing for potential departures from the Normality, Linearity, Homoskedasticity, Independence, and t-invariance assumptions, it is shown that the assumptions implicitly imposed on these empirical asset pricing models are inappropriate. In light of these results, the probabilistic assumptions underlying the CAPM and the Fama-French multi-factor models are replaced with the Studentís t, Linearity, Heteroskedasticity, Markov Dependence, and t-heterogeneity assumptions. The new probabilistic structure results in a family of heterogeneous Studentís t models which are shown to account for all the statistical regularities in the data. This family of models provides an appropriate basis for revisiting the empirical adequacy of the CAPM and the Fama-French multifactor models, as well as other models, such as alternative asset pricing models and risk evaluation models. Along the lines of providing a sound basis for reliable statistical inference results, the proposed models can serve as a coherent basis for selecting the potential sources of risk from a set of possible ones. The latter contributes to the enhancement of the substantive adequacy of the CAPM and the multi-factor models.