The endo-exo problem lies at the heart of statistical identi fication in many fields of science, and is often plagued by spurious strong-and-long memory due to improper treatment of trends, shocks and shifts in the data. A class of models that has shown to be useful in discerning exogenous and...

The statistical estimate of the branching ratio η of the Hawkes model, when fitted to windows of mid-price changes, has been reported to approach criticality (η = 1) as the fitting window becomes large. In this study -- using price changes from the EUR/USD currency pair traded on the...

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...