Change-point detection in causal processes : Applications to the flows of the watershed of the Sanaga in Cameroon
This thesis focuses on the change-point detection in the causal processes with applications to the flows of the watershed of the Sanaga in Cameroon. We consider a class of semi-parametric models that contains the classical causal processes such as AR, ARCH, TARCH. Chapter 1 is a summary of the works. It presents the model with examples and the main results obtained in chapters 2, 3 and 4. Chapter 2 deals with the off-line multiple changes detection using a penalized likelihood criterion. The number of breaks, the dates of breaks and the parameters of model on each segment are unknown. They are estimated by maximizing a contrast based on the quasi-likelihood and penalized by the number of breaks. We suggest a possible choice of penalty parameter and show that the estimators of the parameters of model are consistent with optimal rates. For practical applications an adaptive estimator of the penalty parameter based on the slope heuristic is proposed. A dynamic programming algorithm is used to reduce the computational cost, it is now a $\mathcal {O} (n ^ 2)$ complexity algorithm. Comparisons made with existing results show that our procedure is more stable and robust. Chapter 3 is still the off-line multiple changes detection, but here a test procedure is used. We construct a new procedure that, combined with Itereted Cumulative Sums of Squares (ICSS) type algorithm, is able to detect multiple breaks in causal processes. The test is consistent in power and the comparison with existing procedures shows that it is more powerful. In chapter 4, we study the on-line change detection in the class of semi-parametric model considered in chapters 2 and 3. A procedure based on the quasi-likelihood of the observations was developed. The procedure is consistent in power and the detection delay is better than existing ones. Chapter 5 deals with applications to the flows of the watershed of the Sanaga. The procedures described in chapters 2 and 3 were used by applying an ARMA model after deseasonalization and standardization. Both procedures detected breaks which are "close".