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Title: Estimating change points in nonparametric time series regression models Authors:  Leonie Selk - Helmut-Schmidt-University (Germany) [presenting]
Abstract: A regression model is considered that allows for time-series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that there exists a change point such that the regression function changes at the unknown time $\lfloor ns_0\rfloor$, $s_0\in[0,1]$, and our aim is to estimate the (rescaled) change point $s_0$. The considered estimator is based on a Kolmogorov-Smirnov functional of the marked cumulative sum of residuals. We show the consistency of the estimator and prove a rate of convergence of $O_P(n^{-1})$. Additionally, we investigate the case of lagged dependent covariates, that is, autoregression models with a change in the nonparametric (auto-) regression function and give a consistency result. The method of proof also allows for different kinds of functionals such that Cram\'er-von Mises type estimators can be considered similarly. Finite sample simulations indicate the good performance of our estimator in regression as well as autoregression models and a real data example shows its applicability in practice.