The sum of squared intraday returns provides an unbiased and almost error-free measure of ex-post volatility. In this … paper we develop a nonlinear Autoregressive Fractionally Integrated Moving Average (ARFIMA) model for realized volatility …, which accommodates level shifts, day-of-the-week effects, leverage effects and volatility level effects. Applying the model …

, which reveals an interesting connection to the theory of Brownian excursion areas. A major application is the estimation of … the integrated squared volatility of an effcient price process Xt from intra-day order book quotes. We derive n -1/3 as … optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in …