Joseph, S and Kashyap, LD and Jain, S (2022) Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes. In: Journal of Computational Science, 63 .
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Abstract
The Multi-dimensional Hawkes Process (MHP) is a class of self and mutually exciting point processes that find many applications–from predicting earthquakes to modelling order books in high-frequency trading. This paper makes two significant contributions; we first find an unbiased estimator for the gradient of the Hawkes process's log-likelihood estimator. The estimator enables the efficient implementation of the stochastic gradient descent method for the maximum likelihood estimation. The second contribution is that we propose a specific neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on synthetic and natural datasets and find the method has comparable or better performance than existing estimation methods. The use of neural networks for modelling the excitation kernel ensures that we do not compromise on the Hawkes model's interpretability. At the same time, the proposed algorithm has the flexibility to estimate any non-standard Hawkes excitation kernel.
| Item Type: | Journal Article |
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| Publication: | Journal of Computational Science |
| Publisher: | Elsevier B.V. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Commerce; Gradient methods; Parameter estimation; Stochastic systems, BTC-USD market microstructure; Log likelihood; Log-likelihood estimator; Market microstructures; Multi dimensional; Multidimensional hawkes process; Neural-networks; Non-parametric estimations; Nonparametrics; Shallow neural hawkes, Maximum likelihood estimation |
| Department/Centre: | Division of Interdisciplinary Sciences > Management Studies |
| Date Deposited: | 27 Jul 2022 11:07 |
| Last Modified: | 27 Jul 2022 11:07 |
| URI: | https://eprints.iisc.ac.in/id/eprint/74989 |
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