Title: Detecting changes in the covariance structure of high dimensional time series using random matrix theory
Authors: Sean Ryan - Lancaster University (United Kingdom) [presenting]
Rebecca Killick - Lancaster University (United Kingdom)
Abstract: A novel method is proposed for detecting changes in the covariance structure of high dimensional time series. The approach uses a test statistic that is based on the ``natural'' distance between two covariance matrices. As a result, the performance of this geometrically inspired method does not depend on the underlying structure of the covariance matrix. We demonstrate that this compares favourably with other approaches. Using results from Random Matrix Theory we explore the asymptotic behaviour of our method in the high dimensional setting (i.e. the number of variables is a comparable to the length of the data). We also explore the finite sample performance of our method via a range of simulations.