Abstract :
Recent research has focused on modeling asset prices by Itˆo semimartingales. In
such a modeling framework, the quadratic variation consists of a continuous and a
jump component. This paper is about inference on the jump part of the quadratic
variation, which can be estimated by the difference of realized variance and realized
multipower variation. The main contribution of this paper is twofold. First, it
provides a bivariate asymptotic limit theory for realized variance and realized multipower
variation in the presence of jumps. Second, this paper presents new, consistent
estimators for the jump part of the asymptotic variance of the estimation bias.
Eventually, this leads to a feasible asymptotic theory that is applicable in practice.
Finally, Monte Carlo studies reveal a good finite sample performance of the proposed
feasible limit theory.
