The quadratic variation of a semimartingale plays an important role in a variety of applications, particularly so in financial econometrics, where it is closely linked to volatility.  It contains information pertaining to both continuous and discontinuous path behavior of the underlying process, and separating its continuous and discontinuous parts based on high-frequency observations is a problem that has been tackled through a variety of approaches to-date.
 
However, despite the favorable asymptotic statistical properties of many of these approaches, their use in practice requires heuristic selection of tuning parameters that can greatly impact their estimation performance.
 
In this talk, I will discuss some recent work concerning an iterative approach that circumvents the "tuning problem."
 
This is based on joint work with J. E. Figueroa-López and Y. Han.