We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume...

Capturing dependence among a large number of high dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are...

We introduce a new fractionally integrated model for covariance matrix dynamics based on the long-memory behavior of daily realized covariance matrix kernels and daily return observations. We account for fat tails in both types of data by appropriate distributional assumptions. The covariance...