ONLINE CHANGE-POINT DETECTION FOR MATRIX-VALUED TIME SERIES WITH LATENT TWO-WAY FACTOR STRUCTURE

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.