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Consistency and Computation of Regularized MLEs for Multivariate Hawkes Processes

Probability 2018-10-09 v1 Statistics Theory Statistics Theory

Abstract

This paper proves the consistency property for the regularized maximum likelihood estimators (MLEs) of multivariate Hawkes processes (MHPs). It also develops an alternating minimization type algorithm (AA-iPALM) to compute the MLEs with guaranteed global convergence to the set of stationary points. The performance of this AA-iPALM algorithm on both synthetic and real-world data shows that AA-iPALM consistently improves over iPALM and PALM. Moreover, AA-iPALM is able to identify the causality structure in rental listings on craigslist and herd behavior in the NASDAQ ITCH dataset.

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Cite

@article{arxiv.1810.02955,
  title  = {Consistency and Computation of Regularized MLEs for Multivariate Hawkes Processes},
  author = {Xin Guo and Anran Hu and Renyuan Xu and Junzi Zhang},
  journal= {arXiv preprint arXiv:1810.02955},
  year   = {2018}
}

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46 pages