Online change-point detection for matrix-valued time series with latent two-way factor structure

作者：Yong He, Xin-bing Kong, Lorenzo Trapani, Long Yu · 发表于：Annals of Statistics · 年份：2021 · DOI：10.1214/24-aos2410 · 被引用次数：18 · 研究领域：Mathematics

This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a changepoint. Our procedure is based only on rates; at each point in time, we randomise the estimated eigenvalue, thus obtaining a normally distributed sequence which is $i.i.d.$ with mean zero under the null of no break, whereas it diverges to positive infinity in the presence of a changepoint. We base our monitoring procedures on such sequence. Extensive simulation studies and empirical analysis justify the theory.