Change-in-Covariance Testing in Factor Models and Applications

• Activity Number: 341 - Change-Point Models in Quality Control Applications
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Quality and Productivity Section
• Author(s): Ansgar Steland*
• Companies: RWTH Aachen University
• Keywords: Change-point; Covid-19; CUSUM; High-Dimensional Statistics; Quality Control; Time Series

Abstract

We discuss new methods to test for the presence of a change-point in the covariance matrix of time series covering a wide range of factor models. The tests are suitable for high-dimensional settings and big data. CUSUM-type statistics associated to bilinear forms of the sample covariance matrix are used, which are related to data projections. Methods such as PCA or sparse PCA can be used to analyze for changes in relevant subspaces. The case of many projections is dealt with by a multiple testing approach. The CUSUM statistics are standardized either by LRV estimates or by self-standardization. For complex change-point models for which the classical CUSUM is insensitive, we maximize over all possible subsamples and use a recently established exceedance asymptotics. The methods are investigated by simulations and illustrated by applications to real industrial data. Especially, in view of the Covid-19 crisis, we analyze the impact of the Covid-19 financial crash on the Fama and French factors.