A0519
Title: Asymptotic mixed normality of the realized covariance matrix in high-dimensions
Authors: Yuta Koike - University of Tokyo (Japan) [presenting]
Abstract: Asymptotic mixed normality of the realized covariance matrix for a multi-dimensional continuous semimartingale is established, where the dimension may be much larger than the sample size. More precisely, in such a setting, a mixed normal approximation of the error distribution is shown in terms of the Kolmogorov distance. The proof is based on a variant of the Chernozhukov-Chetverikov-Kato theory on high-dimensional central limit theorems for sums of independent random vectors, where the theory is adapted to random asymptotic covariance matrices with the help of the Malliavin-Stein method. An application to testing for residual sparsity in a continuous-time factor model is presented.
