The Double Gaussian Approximation for High Frequency Data

High frequency data have become an important feature of many areas of research. They permit the creation of estimators in highly non-parametric classes of continuous-time models. In the context of continuous semi-martingale models, we here provide a locally parametric ‘double Gaussian’ approximation, to facilitate the analysis of estimators. As in Mykland and Zhang (2009), the error in the approximation can be offset with a postasymptotic likelihood correction. The current approximation is valid in large neighbourhoods, permitting a sharp analysis of estimators that use local behaviour over asymptotically increasing numbers of observations.