Georgia Institute of Technology College of Sciences

Statistical inference of stochastic processes based on high-frequency observations has been an active research area for more than a decade. The most studied problem is the estimation of the quadratic variation of an Itô semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of truncated moments of Lévy processes, a new efficient estimator is developed for a class of Lévy processes of unbounded variation. The proposed method is based on an iterative debiasing procedure of truncated realized quadratic variations. This is joint work with Cooper Bonience and Yuchen Han.