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

Consistency and Computation of Regularized MLEs for Multivariate Hawkes Processes