Detection of Multiple Structural Breaks in Large Covariance Matrices
Detection of Multiple Structural Breaks in Large Covariance Matrices
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DOI：
10.1080/07350015.2022.2076686
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发表时间：
2022-05
影响因子：
3
通讯作者：
Yu-Ning Li;Degui Li;P. Fryzlewicz
中科院分区：
文献类型：
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作者：
Yu-Ning Li;Degui Li;P. Fryzlewicz
摘要本文研究了满足近似因子模型的高维时间序列大型同期协方差矩阵的多重结构突变。公共分量二阶矩结构的突变是由于因子载荷或潜在因子协方差的突然变化，需要对因子模型进行适当的变换，以便通过经典的主成分分析来估计(转换后的)公共因子和因子载荷。根据估计的因素和特殊误差，引入了一种易于实现的基于累积和的检测技术，以一致地估计断点的位置和数量，并正确地识别它们是源于共同的误差分量还是来自特殊的误差分量。协方差野生二进制分割算法(WBS-CoV)和野生稀疏协方差二进制分割算法(WSBS-CoV)分别用于估计常见误差分量和特殊误差分量中的突变。在一定的技术条件下，推导了该方法的渐近性质，并对估计的中断达到了接近最优的速率(最高可达对数因子)。通过蒙特卡罗模拟研究，检验了该方法的有限样本性能，并将其与其他已有方法进行了比较。最后，我们应用我们的方法研究了S指数成分股日收益率的同期协方差结构，并发现了一些突变，包括发生在2007年至2008年金融危机期间的突变和最近的新冠肺炎疫情。提供了一个“”包来实现所提出的算法。
ABSTRACT This article studies multiple structural breaks in large contemporaneous covariance matrices of high-dimensional time series satisfying an approximate factor model. The breaks in the second-order moment structure of the common components are due to sudden changes in either factor loadings or covariance of latent factors, requiring appropriate transformation of the factor models to facilitate estimation of the (transformed) common factors and factor loadings via the classical principal component analysis. With the estimated factors and idiosyncratic errors, an easy-to-implement CUSUM-based detection technique is introduced to consistently estimate the location and number of breaks and correctly identify whether they originate in the common or idiosyncratic error components. The algorithms of Wild Binary Segmentation for Covariance (WBS-Cov) and Wild Sparsified Binary Segmentation for Covariance (WSBS-Cov) are used to estimate breaks in the common and idiosyncratic error components, respectively. Under some technical conditions, the asymptotic properties of the proposed methodology are derived with near-optimal rates (up to a logarithmic factor) achieved for the estimated breaks. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the developed method and its comparison with other existing approaches. We finally apply our method to study the contemporaneous covariance structure of daily returns of S&P 500 constituents and identify a few breaks including those occurring during the 2007–2008 financial crisis and the recent coronavirus (COVID-19) outbreak. An package “ ” is provided to implement the proposed algorithms.