Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + sigma (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility -- in particular, it gives feasible ways to consistently estimate the asymptotic variance...

Properties of a specification test for the parametric form of the variance function in diffusion processes are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable "x" it is known that the...

We consider a new class of estimators for volatility functionals in the setting of frequently observed Ito diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of...

This paper presents a Hayashi–Yoshida-type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent non-synchronous points. The estimator of the covariation matrix is...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility - in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...