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Title: Change-point testing of high-dimensional spectral density matrices Authors:  Ansgar Steland - RWTH Aachen University (Germany) [presenting]
Abstract: The analysis of multivariate time series in the frequency domain may be based on the spectral density matrix in terms of auto- and cross-spectra and has applications in various areas such as finance, brain research or sensor monitoring. Identifying inhomogeneities in the form of significant change-points (breaks), e.g. in coherences, is a relevant statistical issue, often complicated by the fact that additional structure, such as a factor effect, needs to be taken into account. A flexible framework is proposed to analyze high-dimensional nonlinear time series, which is formally based on self-standardized CUSUM statistics based on localized linear combinations of bilinear forms of spectral average statistics calculated from local lag-window spectral estimators, and, more generally, nonlinear functions of the spectral density matrix. In this way, one can easily analyze contrasts between cross-spectra or coherencies, test for a change in a treatment effect in a frequency band or test the equality of spectral density matrices. All asymptotic results are shown under a general nonlinear time series model. A wild bootstrap procedure is proposed to determine critical values. Simulations indicate that the approach performs well in terms of type I and type II error rates. The method is illustrated by analyzing SP500 returns.