We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower...

We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous...

We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous...

The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the...

Using realized volatility to estimate daily conditional volatility of financial returns, we compare forecasts of daily volatility from standard QML-estimated GARCH models, and from projections on past realized volatilities obtained from high-frequency data. We consider horizons extending to...

We propose two new jump-robust estimators of integrated variance based on highfrequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical...

The contribution of this paper is two-fold. First we show how to estimate the volatility of high frequency log-returns where the estimates are not a affected by microstructure noise and the presence of Lévy-type jumps in prices. The second contribution focuses on the relationship between the...

We call the realized variance (RV), calculated with observed prices contaminated by (market) microstructure noises (MNs), the noise-contaminated RV (NCRV), and refer to the bias component in the NCRV, associated with the MNs, as the MN component. This paper develops a state space method for...

We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an...