Using the Epps effect to detect discrete data generating processes
Etienne Pienaar and
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On different time-intervals it can be useful to empirically determine whether the measurement process being observed is fundamental and representative of actual discrete events, or whether these measurements can still be faithfully represented as random samples of some underlying continuous process. As sampling time-scales become smaller for a continuous-time process one can expect to be able to continue to measure correlations, even as the sampling intervals become very small. However, with a discrete event process one can expect the correlation measurements to quickly break-down. This is a theoretically well explored problem. 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.
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