It is well-known that the conventional CUSUM tests are over-sized in the presence of high persistence and misspecification. In this article, we propose a block wild bootstrap-based CUSUM test (CUSUM-BWB) for detecting changes in mean and variance shifts under possible high persistence and misspecification. We establish the asymptotic properties of the proposed test and our simulation study shows that CUSUM-BWB tests achieve the correct sizes and comparable powers in finite samples. Our method is also applied to the realized volatility of the KOSPI stock index.

中文翻译：

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阻止基于野生引导程序的 CUSUM 测试对高持久性和错误指定具有鲁棒性

众所周知，在存在高持久性和错误规范的情况下，传统的 CUSUM 测试规模过大。在本文中，我们提出了一种基于块野生引导的 CUSUM 测试 (CUSUM-BWB)，用于检测在可能的高持久性和错误指定下的均值和方差变化的变化。我们建立了所提议测试的渐近特性，我们的模拟研究表明，CUSUM-BWB 测试在有限样本中实现了正确的大小和可比的功效。我们的方法也适用于 KOSPI 股票指数的已实现波动率。