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Statistics seminar: Sequential testing for structural stability in approximate factor models

26/10/2017 dalle 14:30 alle 17:00

Dove Dipartimento di Scienze Statistiche - Via Belle Arti 41 - Aula Seminari

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Matteo Barigozzi
London School of Economics

We develop a 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: 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. (Joint work with Lorenzo Trapani)

Giuseppe Cavaliere