Abstract:
We will review some recent results on estimation of the minimal amount of driving motions required to model a d-dimensional price process. The d-dimensional semimartingale is assumed to be observed at high frequency and multivariate Levy process is considered to be the driving motion. We discuss the economic interpretation of this problem and present some ideas/solutions for (a) continuous semimartingales, (b) continuous semimartingales observed with noise and (c) discontinuous semimartingales driven by alpha stable motion.
The talk is based on joint articles with T. Fissler, J. Jacod and M. Rosenbaum.