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Nuisance-parameter-free changepoint detection in non-stationary series
TEST ( IF 1.2 ) Pub Date : 2019-05-03 , DOI: 10.1007/s11749-019-00659-1
Michal Pešta , Martin Wendler

Many changepoint detection procedures rely on the estimation of nuisance parameters (like long-run variance). If a change has occurred, estimators might be biased and data adaptive rules for the choice of tuning parameters might not work as expected. If the data are not stationary, this becomes more challenging. The aim of this paper is to present two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by combing self-normalization and wild bootstrap. We investigate 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. As a by-product, a changepoint estimator is introduced and its consistency is proved. The results are illustrated through a simulation study. The new completely data-driven tests are applied to real data examples from finance and hydrology.

中文翻译:

非平稳序列中无干扰参数的变化点检测

许多变更点检测程序都依赖于干扰参数的估计(例如长期方差)。如果发生了更改,估计器可能会出现偏差,并且用于选择调整参数的数据自适应规则可能无法按预期工作。如果数据不稳定,这将变得更具挑战性。本文的目的是提出两个变更点测试,它们既不涉及烦扰也不涉及调整参数。这是通过结合自我规范化和野生引导程序来实现的。我们研究了渐近行为,并证明了假设和其他假设条件下自举的一致性,假设条件是对时间序列的弱依赖性较弱。作为副产品,引入了变化点估计器,并证明了其一致性。通过仿真研究说明了结果。
更新日期:2019-05-03
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