We consider estimating a factor model for high-dimensional time series that contains structural breaks in the factor loading space at unknown time points. We first study the case when there is one change point in factor loadings, and propose a consistent estimator for the structural break location, whose convergence rate is shown to depend on an interplay between the dimension of the observed time series and the strength of the underlying factor structure. Our results reveal that the asymptotic behavior of the proposed estimator can be asymmetric in the sense that a larger estimation error can occur toward the regime with weaker factor strength. Based on the proposed estimator for the structural break location, we also consider the problem of estimating the factor loading spaces before and after the structural break. We show that the proposed estimators for change-point location and loading spaces are consistent when the numbers of factors are correctly estimated or overestimated. The algorithm for multiple change-point detection is also developed in the paper. Compared with existing results on change-point factor analyses of high-dimensional time series, a distinguished feature of the current paper is that the noise process is not necessarily assumed to be idiosyncratic and as a result we allow the noise process with potentially strong cross-sectional dependence. Another advantage for the proposed method is that it is specifically designed for the changes in the factor loading space and the stationarity assumption is not imposed on either the factor or noise process, while most existing methods for change-point detection of high-dimensional time series with/without a factor structure require the data to be stationary or ’close’ to a stationary process between two change points, which is rather restrictive. Numerical experiments including a Monte Carlo simulation and a real data application are presented to illustrate the proposed estimators perform well.

我们考虑为高维时间序列估计一个因子模型，该模型包含未知时间点因子加载空间中的结构中断。我们首先研究了因子载荷有一个变化点的情况，并提出了结构断裂位置的一致估计量，其收敛速度取决于观察到的时间序列的维度和基础强度之间的相互作用因素结构。我们的结果表明，所提出的估计器的渐近行为可能是不对称的，因为在因子强度较弱的情况下可能会出现较大的估计误差。基于所提出的结构断裂位置估计器，我们还考虑了估计结构断裂前后因子载荷空间的问题。我们表明，当正确估计或高估因素的数量时，所提出的变化点位置和装载空间的估计量是一致的。论文中还开发了多变点检测算法。与现有的高维时间序列变点因子分析结果相比，本文的一个显着特点是噪声过程不一定是特异的，因此我们允许噪声过程具有潜在的强交叉截面依赖性。所提出方法的另一个优点是它是专门为因子加载空间的变化而设计的，并且平稳性假设不强加于因子或噪声过程，而大多数现有的有/没有因子结构的高维时间序列的变化点检测方法都要求数据是平稳的或“接近”两个变化点之间的平稳过程，这是相当有限的。提供了包括蒙特卡罗模拟和实际数据应用在内的数值实验，以说明所提出的估计器性能良好。