Nuisance Parameters Free Changepoint Detection in Non-stationary Series
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Detecting abrupt changes in the mean of a time series, so-called changepoints, is important for many applications. However, many procedures rely on the estimation of nuisance parameters (like long-run variance). Under the alternative (a change in mean), estimators might be biased and data-adaptive rules for the choice of tuning parameters might not work as expected. If the data is not stationary, but heteroscedastic, this becomes more challenging. The aim of this paper is to present and investigate two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by combing self-normalization and wild bootstrap. We study the asymptotic behavior and show the consistency of the bootstrap under the hypothesis as well as under the alternative, assuming mild conditions on the weak dependence of the time series and allowing the variance to change over time. As a by-product of the proposed tests, a changepoint estimator is introduced and its consistency is proved. The results are illustrated through a simulation study, which demonstrates computational efficiency of the developed methods. The new tests will also be applied to real data examples from finance and hydrology.
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