This paper develops a method to improve the estimation of jump variation using high frequency data with the existence of market microstructure noises. Accurate estimation of jump variation is in high demand, as it is an important component of volatility in finance for portfolio allocation,...

This paper presents identification and estimation results for a flexible state space model. Our modification of the canonical model allows the permanent component to follow a unit root process and the transitory component to follow a semiparametric model of a higher‐order...

We consider the problem of smoothing data on two-dimensional grids with holes or gaps. Such grids are often referred to as difficult regions. Since the data is not observed on these locations, the gap is not part of the domain. We cannot apply standard smoothing methods since they smooth over...

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...

The estimation and the analysis of long memory parameters have mainly focused on the analysis of long-range dependence in stock return volatility using traditional time and spectral domain estimators of long memory. The definitive ubiquity and existence of long memory in the volatility of stock...