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Inférence statistique des modèles conditionnellement hétéroscédastiques avec innovations stables, contraste non gaussien et volatilité mal spécifiée

Abstract : In this thesis, we focus on the inference of conditionally heteroskedastic models under different assumptions. This thesis consists of three parts and an introductory chapter. In the first part, we use an alternate identification assumption of the model and we define a non Gaussian quasi maximum likelihood estimator. We show that, under certain conditions, this estimator is more efficient than the Gaussian quasi maximum likelihood estimator. In a second part, we study the inference of a conditionally heteroskedastic model when the process of the innovations is distributed as an alpha stable law. We establish the consistency and the asymptotic normality of the maximum likelihood estimator. Since the alpha stable laws appear in general as a limit, we then focus of the behavior of this same estimator when the law of the innovation process is not stable but in the domain of attraction of a stable law. In the last part of this thesis, we study the estimation of a GARCH model when the data generating process is a conditionally heteroskedastic model whose coefficients are subject to Markov switching regimes. We show that, in a missspecified framework, this estimator converges toward a pseudo true value and we establish its asymptotic properties when this process is non stationary and explosive. Through simulations, we investigate the predictive ability of the missspecified GARCH model. Thus we determinate the robustness of the model and of the estimator of the quasi maximum likelihood to the missspecification of the volatility
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Guillaume Lepage. Inférence statistique des modèles conditionnellement hétéroscédastiques avec innovations stables, contraste non gaussien et volatilité mal spécifiée. Modélisation et simulation. Université Charles de Gaulle - Lille III, 2012. Français. ⟨NNT : 2012LIL30026⟩. ⟨tel-00881518⟩

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