Title: Eigenstructure of sample covariance matrices for high-dimensional heavy-tailed stochastic volatility models
Authors: Thomas Mikosch - University of Copenhagen (Denmark) [presenting]
Johannes Heiny - University of Aarhus (Denmark)
Abstract: The interest is in the asymptotic behavior of the eigenvalues of the sample covariance matrix where the data matrix consists of a $p$-dimensional time series that constitutes a $p\times n$-dimensional stochastic volatility field. We assume that the marginal tails of the data entries have power-law tails with index smaller than four. We focus on the case when the dimension $p$ increases with the sample size $n$. Our main goal is to show that the eigenvalues of the sample covariance matrix are essentially determined by its diagonal elements. We consider limit theory of Poisson-type for the point process of the scaled eigenvalues and also discuss the structure of the corresponding eigenvectors.