Detection of Multiple Structural Breaks in Large Covariance Matrices

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 covaria...

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Bibliographic Details
Published in:Journal of business & economic statistics Vol. 41; no. 3; pp. 846 - 861
Main Authors: Li, Yu-Ning, Li, Degui, Fryzlewicz, Piotr
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects:
Algorithms
Approximate factor models
Binary segmentation
Coronaviruses
CUSUM
Large covariance matrix
Monte Carlo simulation
Principal component analysis
Structural breaks
ISSN:0735-0015, 1537-2707
Online Access:Get full text
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Summary: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.
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ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2022.2076686