Detecting discrete processes with the Epps effect

TL;DR

This paper investigates the Epps effect in high-frequency financial data to determine whether tick data is better modeled as discrete events or as continuous Brownian diffusions, proposing methods to distinguish these representations.

Contribution

It introduces a refined correction for the Epps effect and demonstrates how Hawkes process models better capture high-frequency correlation dynamics than Brownian models.

Findings

Hawkes models recover phenomenology not captured by Brownian models.

A refined method corrects for asynchrony in the Epps effect.

Discrete event representations outperform Brownian diffusions in modeling high-frequency data.

Abstract

The Epps effect is key phenomenology relating to high frequency correlation dynamics in financial markets. We argue that it can be used to provide insight into whether tick data is best represented as samples from Brownian diffusions, or as samples from truly discrete events represented as 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 underlying representations. These in turn demonstrate how a simple Hawkes representation recovers phenomenology reported in the literature that cannot be recovered using a Brownian representation without additional ad hoc model complexity. However, complex ad hoc noise models built on Brownian motions cannot in general be discriminated relative to a Hawkes representation. Nevertheless, we argue that high frequency correlation dynamics are most faithfully recovered when tick data is represented as a web of interconnected discrete events rather than being samples from continuous Brownian diffusions even when combined with noise.