Asbtract
We study a family of test statistics to detect changepoints in a large dimensional, latent factor model. Exploiting the fact that a change in the factor structure can always be re-written as a change in the (finite-dimensional) second moment of the common factors, we propose in particular a family of weighted statistics, which are able to detect breaks occurring very close to the sample endpoints. Technically, our results are based on a strong approximation of partial sums of the sample second moments of the estimated factors. Building on it, we are able to study weighted functionals of the CUSUM process of the aforementioned sample second moments. We also consider the standardised CUSUM process, deriving a Darling-Erdos-type result, and we also propose a class of more heavily weighted CUSUM processes to detect breaks occurring at the very beginning or the very end of the sample. Our strong approximation also allows us to study tests based on the MOSUM process, and to extend our results for in-sample detection of breaks to the case of online, sequential monitoring.
The paper is joint with M. Barigozzi and H. Cho
Invited by: Econometrics Group
Local Organizer: Giovanni Angelini