Detection of abrupt changes and autoregressive models

Abstract : This thesis has two parts: the first part deals the change points problem and the second concerns the weak threshold autoregressive model (TAR); the errors are not correlated.In the first part, we treat the change point analysis. In the litterature, it exists two popular methods: The Penalized Least Square (PLS) and the Filtered Derivative introduced by Basseville end Nikirov.We give a new method of filtered derivative and false discovery rate (FDqV) on real data (the wind turbines and heartbeats series). Also, we studied an extension of FDqV method on weakly dependent random variables.In the second part, we spotlight the weak threshold autoregressive (TAR) model. The TAR model is studied by many authors such that Tong(1983), Petrucelli(1984, 1986). there exist many applications, for example in economics, biological and many others. The weak TAR model treated is the case where the innovations are not correlated.
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Mohamed Abdillahi Elmi. Detection of abrupt changes and autoregressive models. Optics / Photonic. Université Bourgogne Franche-Comté, 2018. English. ⟨NNT : 2018UBFCD005⟩. ⟨tel-01830415⟩

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