  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.
