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

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