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Change-point estimator for nonlinear (auto-)regressive processes using neural network functions
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In this work, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change model and approximate the unknown (auto-)regression function by a neuronal network with one hidden layer.
It is shown that the test has asymptotic power one for a wide range of alternatives not restricted to changes in the mean of the time series. Furthermore, we prove that the corresponding estimator converges to the true change point with the optimal rate and derive the asymptotic distribution. Some simulations illustrate the behavior of the estimator with a special focus on the misspecified case, where the regression function is indeed not given by a neuronal network. Finally, we apply the estimator to some financial data.
Kooperationen: Dr. Stefanie Schwaar, ITWM Kaiserslautern

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