The Double Gaussian Approximation for High Frequency Data


  • This paper is based on a plenary presentation at NORDSTAT Meeting in Voss Norway, June 2010.

  • Microstructure for this purpose means measurement error. The term also has a wider usage; see, for example, O'Hara (1995) and Hasbrouck (1996).

Per A. Mykland, Department of Statistics, The University of Chicago, Chicago, IL 60637, USA. E-mail:;


Abstract  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 (Econometrica, 77, 2009, p. 1403), 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.