Testing for Change Points in Time Series
时间序列变点检验AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究时间序列的均值及其他参数变点，使用CUSUM与自归一化检验，对应结构变化和时间序列。
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时间序列变点检验
- 研究问题
- 如何避免长期方差估计中的带宽选择困难，构造时间序列变点检验，并改善依赖强度变化时的功效表现？
- 方法与思路
- 作者构造考虑变点备择的自归一化CUSUM型检验，并扩展到边际中位数、一阶自相关和特定频带的谱变化。
- 材料陈述的贡献
- 摘要称检验渐近分布不含干扰参数且功效单调，提供多参数统一处理，并通过模拟与真实数据展示有限样本表现。
- 阅读关注点
- 应核对自归一化构造、依赖过程与参数估计条件，以及功效单调性的具体含义、模拟比较和多类参数扩展的限制。
- 阅读边界
- OpenAlex索引未注明稿件版本；摘要未说明完整假设、功效单调性的适用范围及模拟结果，不能据此认定全面优于传统检验。
原文摘要
This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional Kolmogorov–Smirnov test statistic involves a consistent long-run variance estimator, which is needed to make the limiting null distribution free of nuisance parameters. The commonly used lag-window type long-run variance estimator requires to choose a bandwidth parameter and its selection is a difficult task in practice. The bandwidth that is a fixed function of the sample size (e.g., n1/3, where n is sample size) is not adaptive to the magnitude of the dependence in the series, whereas the data-dependent bandwidth could lead to nonmonotonic power as shown in previous studies. In this article, we propose a self-normalization (SN) based Kolmogorov–Smirnov test, where the formation of the self-normalizer takes the change point alternative into account. The resulting test statistic is asymptotically distribution free and its power is monotonic. Furthermore, we extend the SN-based test to test for a change in other parameters associated with a time series, such as marginal median, autocorrelation at lag one, and spectrum at certain frequency bands. The use of the SN idea thus allows a unified treatment and offers a new perspective to the large literature of change point detection in the time series setting. Monte Carlo simulations are conducted to compare the finite sample performance of the new SN-based test with the traditional Kolmogorov–Smirnov test. Illustrations using real data examples are presented.