This talk introduces the concept of Observed Asymptotic Variance (Observed AVAR) in continuous time. The estimator solves the problem of setting standard errors for quite general nonparametric estimators based on time dependent processes in a fixed time horizon. The class of processes covered includes both financial high frequency data, and survival analysis. It is not required that the data process be observed continuously.
Observed AVAR in continuous time is shown to be a continuous-time limit of our earlier concept of observed AVAR. The continuous formulation permits a more transparent interpretation of the estimator, and easier analysis. But most importantly, it is easier to implement. In benign cases, this formulation of observed AVAR does typically not require linear combinations of different scales. One may, however, still invoke such combinations when edge effects are large or the parameter processes are highly volatile.