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Bootstrapping the empirical distribution of a stationary process with change-point. (English) Zbl 1431.62180
Authors’ abstract: When detecting a change-point in the marginal distribution of a stationary time series, bootstrap techniques are required to determine critical values for the tests when the pre-change distribution is unknown. In this paper, we propose a sequential moving block bootstrap and demonstrate its validity under a converging alternative. Furthermore, we demonstrate that power is still achieved by the bootstrap under a non-converging alternative. We follow the approach taken by M. Peligrad [Ann. Probab. 26, No. 2, 877–901 (1998; Zbl 0932.62055)], and avoid assumptions of mixing, association or near epoch dependence. These results are applied to a linear process and are shown to be valid under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients.

MSC:
62G09 Nonparametric statistical resampling methods
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
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