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 \%%DIFDELCMD < \left( %%% r +1%DIFDELCMD < \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 statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich 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 .
We develop a monitoring procedure to detect changes in a large approximate factor model. %DIFDELCMD < \left( %%% %DIFDELCMD < \right) %%% Letting r be the number of common factors , we base our statistics on the fact that the \left( r+1\right) -th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes . Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic , obtaining a sequence of \textit{i.i.d statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections , and tight detection times of change-points .
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