14:0014:45

Ana Timberlake Memorial Lecture
Statistics for highfrequency observations of a process Jean Jacod The aim of this talk is to give a quick overview of some recent results in statistics of processes
(with mostly financial time series in mind), in the case of discrete observations of an underlying
process (typically a logprice) over a fixed 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 consistent
estimators as the observation frequency increases, for some specific characteristics of the process.
We 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 underlying processes that
are Itô semimartingale, as it is the case for virtually all continuous time models for logprices, we
will explain in some details how to estimate the volatility, and hopefully (if time permits) how
to decide whether the process is continuous or not, and how to estimate the degree of activity of
jumps, including statements about the rateoptimality and in some cases asymptotic efficiency. For
simplicity, most results will be given when the observation scheme is regular and without noise, but
we will also quickly explain how this can be extended to the case of irregularly spaced observations
times, and the case where the microstructure noise is present. Jean Jacod's keynote address
