In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution theory comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where the proposed test has power, and results in stable power performance when breaks are sparse in the alternative hypothesis. Furthermore, we impose a latent group structure on the subjects with heterogeneous break points and introduce an easy-to-implement clustering algorithm with an information criterion to consistently estimate the unknown group number and membership. The estimated group structure can subsequently improve the convergence property of the post-clustering break point estimate. Monte-Carlo simulation studies and empirical applications show that the proposed estimation and testing techniques have satisfactory performance in finite samples.

翻译：本文中，我们考虑在允许跨部分协方差和时间相关的高维函数时间序列的异质性均值函数中，探测和估计突变。该文章提出了一个新的测试统计量，将函数CUSUM统计量和功率增强成分相结合，其渐近零分布理论可与单个函数时间序列的传统CUSUM理论相媲美。特别地，额外的功率增强成分扩大了该测试具有功效的区域，在备择假设中，其结果稳定且拥有良好的功率性能，使得突变很少。此外，我们在具有异质性突变点的个体上施加一种潜在的组结构，并使用信息准则引入一种易于实施的聚类算法来一致地估计未知的组数和成员资格。估计得到的组合结构随后可以提高聚类后的突变点估计的收敛性质。蒙特卡罗模拟研究和实证应用显示，所提出的估计和测试技术具有令人满意的有限样本性能。