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In this paper, we consider the CUSUM estimator based on  α -mixing sequences. By giving the consistency estimators for mean and covariance functions, the limit distribution of CUSUM estimator is presented as a standard Brownian bridge, which can be used in the change point detection. As applications, some simulations and real data examples are illustrated to test our CUSUM estimator.

The asymptotic distribution of CUSUM estimator based on α -mixing sequences