Autoregressive time series threshold models.

Summary This work is based on the introduction of thresholds in time series models. We start by presenting the theory of homogeneous Markov chains, necessary for the study of nonlinear processes. Autoregressive models of order one with a threshold are the subject of the second part. Distributional properties are obtained in the neighborhood of the linear model, which allows to obtain approximate formulas for various quantities: mean, variance, moments... . Finally, two methods for testing the linearity hypothesis are proposed. The next part proposes a new class of ARCH (autogressive conditionally heteroskedastic) models. The introduction of thresholds in the specification of the conditional variance allows to take into account specific effects on the volatility (persistence, asymmetry according to the sign of the prior errors...). A complete study is proposed: weak stationarity, strict stationarity, computation of moments, analysis of the leptokurtic effect, comparison with ARCH models, estimation of various parameters, test of the homoscedasticity hypothesis. Finally, the last part of the thesis deals with the transition to continuous time of heteroscedastic threshold models.