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.
After revision:  Here we concern ourselves with a simulation based empirical investigation that uses the Epps effect arising from asynchrony and provide a refined method to correct for the effect. The correction is compared against two existing methods correcting for asynchrony. We propose three experiments to discriminate between possible underlying representations: whether the data is best thought to be generated by discrete connected events (as proxied by 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.