Detecting discrete processes with the Epps effect

The Epps effect relates the mechanics of high frequency markets to the observed correlation dynamics. We argue that it can be used to provide insight into whether tick data is best represented as samples from Brownian motions (diffusions), or as samples from truly discrete events generated by connected point processes. We derive the Epps effect arising from asynchrony and provide a refined method to correct for the effect. We then propose three experiments which show how to discriminate between possible representations of the underlying process. These in turn demonstrate how a simple Hawkes representation recovers phenomenology reported in the literature that cannot be recovered using a Brownian representation without the addition of ad hoc model complexity, albeit subject to the limitation that complex ad hoc noise models built on Brownian motions cannot in general be discriminated relative to a Hawkes representation.