On estimation of quadratic variation for multivariate pure jump semimartingales

In this paper we present the asymptotic analysis of realised quadratic variation for multivariate symmetric β-stable Lévy processes, β∈(0,2), and certain pure jump semimartingales. The main focus is on derivation functional limit theorems its spectrum. We will show that limiting process a matrix-valued when original β-stable, while conditionally in case integrals with respect to locally motions. These results are mostly related work (Diop et al., 2013), which investigates univariate version problem. Furthermore, implications estimation eigenvalues eigenvectors matrix, useful result principle component analysis. Finally, propose consistent subsampling procedure setting obtain confidence regions.