We discuss inference on the Lévy measure in case of noisy observations. An extension of the pre-averaging method allows for a consistent estimation of the associated spectral function. The asymptotic behaviour of the novel estimator is the same as without noise.

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional...

This paper presents limit theorems for certain functionals of semimartingales observed at high frequency. In particular, we extend results from Jacod (2008) [5] to the case of bipower variation, showing under standard assumptions that one obtains a limiting variable, which is in general...

Central limit theorem, quadratic variation, bipower variation

In this paper we present two new tests for the parametric form of the variance function in difusion processes dXt = b(t;Xt)+ó(t;Xt)dWt: Our approach is based on two stochastic processes of the integrated volatility. We prove weak convergence of these processes to centered processes whose...