Sequential Testing for Structural Stability in Approximate Factor Models

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We develop a a family of monitoring procedures to detect a change in a large factor model. Our statistics are based on the following property of the (r+1)-th eigenvalue of the sample covariance matrix of the data: 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 does not have a known limiting distribution 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-squared 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.