We consider a nonparametric heteroscedastic time series regression model and suggest testing procedures to detect changes in the conditional variance function. The tests are based on a sequential marked empirical process and thus combine classical CUSUM tests with marked empirical process approaches known from goodness-of-fit testing. The tests are consistent against general alternatives of a change in the conditional variance function, a feature that classical CUSUM tests are lacking. We derive a simple limiting distribution and in the case of univariate covariates even obtain asymptotically distribution-free tests. We demonstrate the good performance of the tests in a simulation study and consider exchange rate data as a real data application.

中文翻译：

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非参数波动率变化检测

我们考虑非参数异方差时间序列回归模型并建议测试程序以检测条件方差函数的变化。这些测试基于连续的标记经验过程，因此将经典的 CUSUM 测试与从拟合优度测试中已知的标记经验过程方法相结合。这些测试与条件方差函数变化的一般替代方案一致，这是经典 CUSUM 测试所缺乏的特征。我们推导出一个简单的极限分布，在单变量协变量的情况下，甚至可以获得渐近无分布的测试。我们在模拟研究中证明了测试的良好性能，并将汇率数据视为实际数据应用。