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Lorenzo TRAPANI (University of Leicester School of Business) – “Changepoint Detection in Large Factor Models”
Finance & Financial Econometrics :
Time: 10.30 am
Date: 13th of April 2023
Lorenzo TRAPANI (University of Leicester School of Business) “Changepoint Detection in Large Factor Models”
Abstract :We study changepoint detection in a large factor model, proposing both offline and online detection methods. In all cases, we build on the idea that, in a factor model, under the maintained assumption of the homoscedasticity of the common factors, in the presence of a changepoint the second moment matrix of the common factors changes. Hence, a high-dimensional problem can be conveniently cast into a low-dimensional problem, based on checking for breaks in the second moment matrix of the estimated common factors. Our results build on a maximal inequality for the partial sums of the second moment matrix of the estimated common factors. By virtue of this, we are able to derive strong invariance principles for the partial sums of the estimated second moment matrix of the common factors. Hence, we propose a family of weighted CUSUM statistics for the offline detection of change points, including the standardised CUSUM process (for which we derive a Darling-Erdos theorem) and even more heavily weighted statistics. Our tests have power versus breaks occurring also close to the sample endpoints. We further study the asymptotics of the MOSUM process, and of the maximally selected LR statistic. In addition, we investigate the problem of sequential, online detection of changepoints, proposing a family of detectors which ensure procedure-wise size control and short detection delays; as a by-product, we derive the limiting distribution of the detection delay.
Joint work M Barigozzi and H Cho
Jean-Michel ZAKOIAN (CREST)