Intraday and high frequency time series are mostly defined by a non-continuous prices process. This paper introduces an integer based ARMA model found to be a better predictor for absolute intraday price changes than continuous time estimators (such as GARCH or multiplicative error models)....

We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Pengs G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian...