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ESTIMATION OF A HIGH-DIMENSIONAL COUNTING PROCESS WITHOUT PENALTY FOR HIGH-FREQUENCY EVENTS

Published online by Cambridge University Press:  14 June 2022

Luca Mucciante
Affiliation:
Royal Holloway University of London
Alessio Sancetta*
Affiliation:
Royal Holloway University of London
*
Address correspondence to Alessio Sancetta, Department of Economics, Royal Holloway University of London, Egham TW20 0EX, UK; e-mail: asancetta@gmail.com.
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Abstract

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This paper introduces a counting process for event arrivals in high-frequency trading, based on high-dimensional covariates. The novelty is that, under sparsity conditions on the true model, we do not need to impose any model penalty or parameters shrinkage, unlike Lasso. The procedure allows us to derive a central limit theorem to test restrictions in a two-stage estimator. We achieve this by the use of a sign constraint on the intensity which necessarily needs to be positive. In particular, we introduce an additive model to extract the nonlinear impact of order book variables on buy and sell trade arrivals. In the empirical application, we show that the shape and dynamics of the order book are fundamental in determining the arrival of buy and sell trades in the crude oil futures market. We establish our empirical results mapping the covariates into a higher-dimensional space. Consistently with the theoretical results, the estimated models are sparse in the number of parameters. Using this approach, we are also able to compare competing model hypotheses on the basis of an out-of-sample likelihood ratio type of test.

Type
ARTICLES
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are very grateful to the Editor (Peter Phillips), the Co-Editor (Eric Renault), the Associate Editor, and the Referees for their detailed comments that have led to substantial improvements both in content and presentation.

References

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