A0952
Title: Inference and change-point testing of high-dimensional spectral density matrices: Beyond spectral averages
Authors: Ansgar Steland - RWTH Aachen University (Germany) [presenting]
Abstract: A flexible approach is studied to analyze high-dimensional nonlinear time series based on linear statistics calculated from spectral average statistics of bilinear forms and nonlinear transformations of lag-window (i.e. band-regularized) spectral density matrix estimators. That class of statistics includes, among others, smoothed periodograms, nonlinear statistics such as coherency, long-run-variance estimators and statistics related to factorial effects as special cases. The novel class of spectral averages of nonlinear functions of the spectral density matrix is introduced. Big data settings are considered by studying sparse sampling. Optimal rate Gaussian approximations are derived for non-stationary nonlinear time series. For change-testing (self-standardized), CUSUM statistics are examined. Further, a specific wild bootstrap procedure is proposed to estimate critical values. A simulation study studies finite sample properties of the proposed self-standardized CUSUM bootstrap testy. The results indicate that the procedure keeps the nominal significance level and performs well under a change-point alternative. The approach is illustrated by analyzing SP500 financial returns from 2016 to 2022, considering a certain well-diversified buy-and-hold portfolio investing 50\% in the minimal-variance portfolio, 25\% in health care, 10\% in Tech firms and 15\% in industrial companies. The results show that all significant change points correspond to real market turmoils.
