Title: Statistics for high-frequency observations of a stochastic process
Authors: Jean Jacod - Universite Paris VI (France) [presenting]
Abstract: It is often the case that one has to do statistical inference for a stochastic process, based on the observation of a single path of the process, at discrete times and over a finite time interval: in such a framework, estimating the law of the process is usually not feasible, but it is often the case that one can still have reasonable estimators, even consistent ones as the observation frequency increases, for some specific characteristics of the process. We will start with a quick review of those characteristics that can be consistently estimated within this framework, versus those which cannot. Then, restricting our attention to the estimation of the volatility in the case of an Ito semimartingale, we will explain some recent developments and new results, including statements about the rate-optimality and in some cases asymptotic efficiency.