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We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests from change point analysis with marked empirical process approaches known from goodness‐of‐fit testing. The tests are consistent against general alternatives of a change in the conditional variance function, a feature that classical CUSUM tests are lacking. We derive a simple limiting distribution and in the case of univariate covariates even obtain asymptotically distribution‐free tests. We demonstrate the good performance of the tests in a simulation study and consider exchange rates as a real data application. [ABSTRACT FROM AUTHOR]

In this paper we consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown time ⌊ n s 0 ⌋ , s 0 ∈ (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 empirical process of residuals. We show consistency of the estimator and prove a rate of convergence of O P (n - 1) which in this case is clearly optimal as there are only n points in the sequence. 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 Cramér-von Mises type estimators can be considered similarly. The approach extends existing literature by allowing nonparametric models, time series data as well as heteroscedasticity. 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 practise. [ABSTRACT FROM AUTHOR]