Central limit theorems for approximate quadratic variations of pure jump Itô semimartingales
In this work central limit theorems for the discretization error of the quadratic variation are developed. The authors focus on Itô semimartingales with vanishing continuous martingale part and the discrete-time approximation of quadratic variation from regularly spaced high-frequency observations. Functional central limit theorems are established for two distinct cases. For processes of finite variation involving a drift the discretization error from n observations converges with rate n to a limiting process which comprises a term induced by the drift and a cross term induced by jumps and the drift. For infinite variation processes or a vanishing drift different rates of convergence and limiting processes are deduced.
scientific article; zbMATH DE number 6142012