This paper develops the necessary methodology for high frequency ANOVA, which includes the estimations of idiosyncratic volatility and realized R-Squared. Because the residual process is latent in the high frequency regression, the estimation of idiosyncratic volatility is notoriously difficult...

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...

We show that the Truncated Realized Variance (TRV) of a semimartingale asset price converges to zero when observations are contaminated by microstructure noises. Under the additive iid noise assumption, a central limit theorem is also proved. In consequence it is possible to construct a feasible...

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove...