We present a fast, accurate estimation method for multivariate Hawkes self-exciting point processes widely used in seismology, criminology, finance and other areas. There are two major ingredients. The first is an analytic derivation of exact maximum likelihood estimates of the nonparametric triggering density. We develop this for the multivariate case and add regularization to improve stability and robustness. The second is a moment-based method for the background rate and triggering matrix estimation, which is extended here for the spatiotemporal case. Our method combines them together in an efficient way, and we prove the consistency of this new approach. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media.

中文翻译：

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多元时空霍克斯过程的快速估计与网络重构

我们为广泛应用于地震学、犯罪学、金融学和其他领域的多元霍克斯自激点过程提出了一种快速、准确的估计方法。有两个主要成分。第一个是非参数触发密度的精确最大似然估计的分析推导。我们为多变量情况开发了这个，并添加了正则化以提高稳定性和鲁棒性。第二种是用于背景速率和触发矩阵估计的基于矩的方法，这里针对时空情况进行了扩展。我们的方法以一种有效的方式将它们结合在一起，我们证明了这种新方法的一致性。大量的数值实验，使用合成数据和现实世界的社交网络数据，表明我们的方法提高了准确性，主流估计方法的可扩展性和计算效率。此外，它极大地提高了基于霍克斯过程的模型在社交网络重建方面的性能，并有助于了解社交媒体上的时空触发动态。