We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work [4] we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the...

Motivated by features of low latency data in finance we study in detail discrete-valued Levy processes as the basis of price processes for high frequency econometrics. An important case of this is a Skellam process, which is the difference of two independent Poisson processes. We propose a...