Before revision:  Here we concern ourselves with a simulation based empirical investigation that uses the Epps effect as a discriminator between situations where the underlying system is discrete e.g. a D-type Hawkes process , and when it can still be appropriate to represent the problem with a continuous-time random process that is being asynchronously sampled e. g. an asynchronously sampled set of correlated Brownian motions. We derive a method aimed to compensate for the Epps effect from asynchrony and then use this to discriminate. We are able to compare the correction on a simple continuous Brownian price path model with a Hawkes price model when the sampling is either a simple homogeneous Poisson Process or a Hawkes sampling process. This suggests that Epps curves can sometimes provide insight into whether discrete data are in fact observables realised from fundamental co-dependent discrete processes, or when they are merely samples of some correlated continuous-time process .
After revision:  Here we concern ourselves with a simulation based empirical investigation that uses the Epps effect as a discriminator between situations where the underlying system is discrete e.g. a D-type Hawkes process ), or if they can be approximated to arise from Brownian diffusions, with or without jumps. We then demonstrate how the Hawkes representation easily recovers the phenomenology reported in the literature; phenomenology that cannot be recovered using a Brownian representation, without additional ad-hoc model complexity, even with jumps. The experiments are applied to trade and quote data from the Johannesburg Stock Exchange. We find evidence suggesting that high frequency correlation dynamics are most faithfully recovered when tick-by-tick data is represented as a web of inter-connected discrete events rather than sampled or averaged from underlying continuous Brownian diffusions irrespective of whether or not they are dressed with jumps .