A parameter estimation method for multivariate aggregated Hawkes processes

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Title: A parameter estimation method for multivariate aggregated Hawkes processes
Authors: Shlomovich, L
Cohen, E
Adams, N
Item Type: Journal Article
Abstract: It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from limitations on recording capabilities and the expense of storing high volumes of precise data. In order to gain a better understanding of the relationships between processes, we consider modelling the aggregated event data using multivariate Hawkes processes, which offer a description of mutually-exciting behaviour and have found wide applications in areas including seismology and finance. Here we generalise existing methodology on parameter estimation of univariate aggregated Hawkes processes to the multivariate case using a Monte Carlo Expectation-Maximization (MCEM) algorithm and through a simulation study illustrate that alternative approaches to this problem can be severely biased, with the multivariate MCEM method outperforming them in terms of MSE in all considered cases.
Date of Acceptance: 13-Jun-2022
URI: http://hdl.handle.net/10044/1/97479
ISSN: 0960-3174
Publisher: Springer
Journal / Book Title: Statistics and Computing
Copyright Statement: Copyright reserved
Keywords: Statistics & Probability
0104 Statistics
0802 Computation Theory and Mathematics
Publication Status: Accepted
Embargo Date: Embargoed for 12 months after publication date
Appears in Collections:Statistics