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 .
The Epps effect is key phenomenology relating to high frequency correlation dynamics in the financial markets. We argue that it can be used to determine whether trades at a tick-by-tick scale are best represented as samples from a Brownian diffusion, perhaps dressed with jumps; or as samples from truly discrete events represented as connected point processes. This can answer the question of whether correlations are better understood as an emergent time scale dependent property. In other words: Is the Epps effect a bias? To this end, we derive 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 ), 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 .
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On different time-intervals
The Epps effect is key phenomenology relating to high frequency correlation dynamics in the financial markets. We argue that
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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
used to determine whether trades at a tick-by-tick scale are best represented as samples from a Brownian diffusion, perhaps dressed with jumps; or as samples from truly discrete events represented as connected point processes. This can answer the question of whether correlations are better understood as an emergent time scale dependent property. In other words: Is the Epps effect a bias? To this end, we derive
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as a discriminator between situations where the underlying system is discrete e.g.
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
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, 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
), 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