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Uncovering causality from multivariate Hawkes integrated cumulants. (English) Zbl 1472.62076

Summary: We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. As a consequence, it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows us to prove that this new estimation technique is consistent. Moreover, we show, on numerical experiments, that our approach is indeed very robust with respect to the shape of the kernels and gives appealing results on the MemeTracker database and on financial order book data.

MSC:

62H12 Estimation in multivariate analysis
62G05 Nonparametric estimation
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Software:

AdaGrad; TensorFlow
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Full Text: arXiv Link

References:

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