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arXiv · 1810.02955

Consistency and Computation of Regularized MLEs for Multivariate Hawkes Processes

Xin Guo·Anran Hu·Renyuan Xu·Junzi Zhang
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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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BibTeXRIS

Xin Guo, Anran Hu, Renyuan Xu, Junzi Zhang. 2018-10-06. Consistency and Computation of Regularized MLEs for Multivariate Hawkes Processes. https://arxiv.org/abs/1810.02955

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