La complexité des marchés financiers et la recrudescence des crises particulièrement sévères contribuent à l'évolution et à la remise en cause de modèles économétriques dits standards dans l'explication et la prévision des dynamiques financières. L'alerte donnée conjointement par les responsables prudentiels et les chercheurs vise à encourager le développement de modèles plus complexes, non linéaires et largement inspirés d'autres disciplines. Nous soutenons dans cette thèse l'idée qu'une approche chaos-stochastique des chroniques financières est susceptible de conduire à de meilleurs résultats. La pertinence de cette association est évaluée pour le risque de marché dans deux cadres d'analyse distincts. Nous montrons tout l'intérêt d'une synthèse des modèles chaotiques et des spécifications GARCH avec ou sans changements de régimes markoviens (MRS) pour la modélisation et la prévision de la Value-at-Risk des indices boursiers de la zone euro. Il ressort de cette étude de meilleurs résultats des modèles chaos-stochastiques et dans le cas des spécifications MRS-GARCH, une meilleure adéquation du modèle chaotique de Lasota(1977) pour les indices de l'Europe du Sud, particulièrement plus volatiles que ceux de l'Europe du Nord pour lesquels nous recommandons le modèle de Mackey-Glass(1977). Cette combinaison permet, dans un cadre bivarié, de mieux appréhender les liens qui existent entre les différentes places boursières de la zone euro. Nous introduisons deux nouvelles spécifications qui intègrent les problématiques liées aux ruptures de corrélations : la première permet de distinguer, par une analyse en sous-périodes, les relations d'interdépendance par rapport aux phénomènes de contagion et la seconde propose, dans un cadre unifié, d'intégrer les ruptures de corrélations. Cette double analyse met en évidence le rôle moteur du couple d'indices franco-allemand, l'existence de deux sphères distinctes constituées d'une part par les indices de l'Europe du Nord et d'autre part par les pays de l'Europe du Sud et l'intensification de certaines relations entre indices suite à la crise des dettes souveraines. Nous constatons et insistons sur la pertinence d'un modèle chaotique en moyenne pour rendre compte d'une part de la volatilité attribuée, à tort, aux effets GARCH. / The complexity of financial markets and the resurgence of severe crises contribute to the skepticism and evolution of standard econometric models in the explanation and prediction of financial time series. The warning given jointly by prudential authorities and researchers aims to encourage the development of nonlinear and more complex models inspired by other disciplines. I argue in this thesis that a chaos-stochastic approach of financial dynamics is likely to lead to better results. The relevance of this association is evaluated for market risk in two distinct analytical frameworks. I show the improvements given by a synthesis of chaotic models and GARCH specifications with or without Markov Regime Switching (MRS) for modelling and predicting the Value-at-Risk of 7 mains index of Monetary and Economic Union. It appears, from this study, better results from chaos-stochastic models. In the case of the MRS-GARCH specifications, I find more adequacy of the chaotic model of Lasota (1977) for the indices of Southern Europe, which are especially more volatile than those of Northern Europe for which I recommend the model of Mackey-Glass (1977). This combination allows, in a bivariate framework, to provide information on the relationship between these different indices. I introduce two new specifications that integrate issues related to correlation breakdowns. The first distinguishes, by a sub-periods analysis, the relations of interdependence of contagious relationships. Meanwhile, the second provides, in a unified framework, an integration of correlations breakdowns. These two analyses imply It appears from this double analysis the leading role of the Franco-German duo, the existence of two distinct spheres formed in a part by the Northern European indices and in another part by countries of the Southern Europe, and the intensification of relations between some indices following the sovereign debt crisis. Finally, these results support the relevance of a chaotic model which may account for some volatilities that are, wrongly, attributed to GARCH effects.

Time series prediction techniques have been used in many real-world applications such as financial market prediction, electric utility load forecasting, weather and environmental state prediction, and reliability forecasting. The underlying system models and time series data generating processes are generally complex for these applications and the models for these systems are usually not known a priori. Accurate and unbiased estimation of time series data produced by these systems cannot always be achieved using well known linear techniques, and thus the estimation process requires more advanced time series prediction algorithms. One type of time series interpolation and prediction algorithm that has been proven to be effective for these various types of applications is Support Vector Regression (SVR) [1], which is based on the Support Vector Machine (SVM) developed by Vapnik et al. [2, 3]. The underlying motivation for using SVMs is the ability of this methodology to accurately forecast time series data when the underlying system processes are typically nonlinear, non-stationary and not defined a-priori. SVMs have also been proven to outperform other non-linear techniques including neural-network based non-linear prediction techniques such as multi-layer perceptrons. As with most time series prediction algorithms, there are typically challenges associated in applying a given heuristic to any general problem. One difficult challenge in using SVR to solve these types of problems is the selection of free parameters associated with the SVR algorithm. There is no given heuristic to select SVR free parameters and the user is left to adjust these parameters in an ad hoc manner. The focus of this dissertation is to present an alternative to the typical ad hoc approach of tuning SVR for time series prediction problems by using Particle Swarm Optimization (PSO) to assist in the SVR free parameter selection process. Developed by Kennedy and Eberhart [4-8], PSO is a technique that emulates the process living creatures (such as birds or insects) use to discover food resources at a given geographic location. PSO has been proven to be an effective technique for many different kinds of optimization problems [9-11]. The focus of this dissertation is to present an alternative to the typical ad hoc approach of tuning SVR for time series prediction problems by using Particle Swarm Optimization (PSO) to assist in the SVR free parameter selection process. Developed by Kennedy and Eberhart [4-8], PSO is a technique that emulates the process living creatures (such as birds or insects) use to discover food resources at a given geographic location. PSO has been proven to be an effective technique for many different kinds of optimization problems [9-11].