Sequential testing for structural stability in approximate factor models

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 (r + 1)-th eigenvalue of the sample covariance matrix of the data (having defined r as the number of common factors): whilst under the null the (r + 1)-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 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.