High frequency data is nowadays commonly observed in various applied sciences. The notion of high frequency refers to the sampling scheme, where the distance between two consecutive observations converges to zero while the total interval remains fixed. We will present some (incomplete) overview about limit theory for high frequency observations for different classes of processes, such as e.g.semimartingales, and their use in statistics.

A major part of the lecture will be devoted to some recent developments in the framework of Levy moving average processes.