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

Abstract

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, the number of spiked eigenvalues in the second moment matrix of the data increases (e.g., in the presence of a change in the loadings, or if a new factor emerges). 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 nonspiked 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. An R package implementing the procedure is available on CRAN. ( https://cran.r-project.org/web/packages/OLCPM/index.html.)