This paper presents a goodness-of-fit test for the volatility function of a SDE driven by a Gaussian process with stationary and centered increments. Under rather weak assumptions on the Gaussian process, we provide a procedure for testing whether the unknown volatility function lies in a given...

In this paper we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing....

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in...

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 nonsynchronous points. The estimator of the covariation matrix is...

This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We...

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general...

In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary (BSS) processes. More precisely, we will show that singularities in the weight function, which is one of the ingredients of a BSS process, may lead to non-standard limits of the...

In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high...

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...

We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work [4] we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the...