Speed of convergence of the threshold estimator of integrated variance

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the threshold estimator is able to separate the integrated variance from the sum of the squared jumps. This has importance in measuring and forecasting the asset risks. The exact convergence speed was found in the literature only when the jumps are of finite variation. Here we give the speed even in presence of infinite variation jumps, as they appear e.g. in some cgmy plus diffusion models.