Online Change-point Detection for Matrix-valued Time Series with Latent Two-way Factor Structure

This paper proposes a novel methodology for the online detectionof changepoints in the factor structure of large matrix time series. Ourapproach is based on the well-known fact that, in the presence of achangepoint, the number of spiked eigenvalues in the second momentmatrix of the data increases (e.g., in the presence of a change in theloadings, or if a new factor emerges). Based on this, we propose twofamilies of procedures - one based on the fluctuations of partial sums,and one based on extreme value theory - to monitor whether the firstnon-spiked eigenvalue diverges after a point in time in the monitoringhorizon, thereby indicating the presence of a changepoint. Our proce-dure is based only on rates; at each point in time, we randomise theestimated eigenvalue, thus obtaining a normally distributed sequencewhich isi.i.d.with mean zero under the null of no break, whereasit diverges to positive infinity in the presence of a changepoint. Webase our monitoring procedures on such sequence. Extensive simula-tion studies and empirical analysis justify the theory. An R packageimplementing the procedure is available on CRAN.