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Revisiting the Epps effect using volume time averaging: An exercise in R

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 نشر من قبل Patrick Chang
 تاريخ النشر 2019
  مجال البحث مالية
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We revisit and demonstrate the Epps effect using two well-known non-parametric covariance estimators; the Malliavin and Mancino (MM), and Hayashi and Yoshida (HY) estimators. We show the existence of the Epps effect in the top 10 stocks from the Johannesburg Stock Exchange (JSE) by various methods of aggregating Trade and Quote (TAQ) data. Concretely, we compare calendar time sampling with two volume time sampling methods: asset intrinsic volume time averaging, and volume time averaging synchronised in volume time across assets relative to the least and most liquid asset clocks. We reaffirm the argument made in much of the literature that the MM estimator is more representative of trade time reality because it does not over-estimate short-term correlations in an asynchronous event driven world. We confirm well known market phenomenology with the aim of providing some standardised R based simulation tools.



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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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Time and the choice of measurement time scales is fundamental to how we choose to represent information and data in finance. This choice implies both the units and the aggregation scales for the resulting statistical measurables used to describe a fi nancial system. It also defines how we measure the relationship between different traded instruments. As we move from high-frequency time scales, when individual trade and quote events occur, to the mesoscales when correlations emerge in ways that can conform to various latent models; it remains unclear what choice of time and sampling rates are appropriate to faithfully capture system dynamics and asset correlations for decision making. The Epps effect is the key phenomenology that couples the emergence of correlations to the choice of sampling time scales. Here we consider and compare the Epps effect under different sampling schemes in order to contrast three choices of time: calendar time, volume time and trade time. Using a toy model based on a Hawkes process, we are able to achieve simulation results that conform well with empirical dynamics. Concretely, we find that the Epps effect is present under all three definitions of time and that correlations emerge faster under trade time compared to calendar time, whereas correlations emerge linearly under volume time.
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