Detection of Multiple Structural Breaks in Large Covariance Matrices

TY - JOUR

T1 - Detection of Multiple Structural Breaks in Large Covariance Matrices

AU - Li, Yu-Ning

AU - Li, Degui

AU - Fryzlewicz, Piotr

N1 - © 2022 The Author(s)

PY - 2023/6/13

Y1 - 2023/6/13

N2 - This paper 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 ofWild 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 R package “BSCOV” is provided to implement the proposed algorithms.

AB - This paper 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 ofWild 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 R package “BSCOV” is provided to implement the proposed algorithms.

U2 - 10.1080/07350015.2022.2076686

DO - 10.1080/07350015.2022.2076686

M3 - Article

SN - 0735-0015

VL - 41

SP - 846

EP - 861

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

IS - 3

ER -