Title: Sequential testing for structural stability in approximate factor models,
Abstract: We develop an on-line monitoring procedure to detect a change in a large
approximate factor model. Our statistics are based on a well-known property of
the $% \left( r+1\right) $-th eigenvalue of the sample covariance matrix of the
data (having defined $r$ as the number of common factors): whilst under the
null the $\left( r+1\right) $-th eigenvalue is bounded, under the alternative
of a change (either in the loadings, or in the number of factors itself) it
becomes spiked. Given that the sample eigenvalue cannot be estimated
consistently under the null, we regularise the problem by randomising the test
statistic in conjunction with sample conditioning, obtaining a sequence of
\textit{i.i.d.}, asymptotically chi-square statistics which are then employed
to build the monitoring scheme. Numerical evidence shows that our procedure
works very well in finite samples, with a very small probability of false
detections and tight detection times in presence of a genuine change-point.