Newest papers

Common Signals, Spurious Cross-Excitation, and Identification in Multivariate Hawkes Processes

Jiwon Jung, Kiseop Lee · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.19428 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

多变形霍克斯模型被广泛用于测量事件数据中的内在相互作用,但隐藏的常见信号可以产生明显的兴奋,即使没有结构相互作用。我们特征结果的线性投射,构建稳定的,非负性霍克斯过程,这些过程在两维和三维系统中共享平均强度和Bartlett频谱的共同信号模型,尽管具有不同的兴奋机制。这会建立第二类不识别的具体形式。我们从霍克斯进程中获得集成的第三类累积,并建立了在两个和三维系统中正常化的结构参数的通用局部识别。 一个准确的对等性蒙特卡罗实验显示了如何区分第三类信息的机制,具有相同的第二类结构,同时在信号下揭示了可识别的实质有限

Machine translation (Meta M2M100); the English original follows.

Abstract

Multivariate Hawkes models are widely used to measure endogenous interactions in event data, but latent common signals can generate apparent excitation even without structural interaction. We characterize the resulting linear projection and construct stable, nonnegative Hawkes processes that share the mean intensity and Bartlett spectrum of common-signal models despite having different excitation mechanisms. This establishes a concrete form of second-order non-identification. We derive integrated third-order cumulants for Hawkes processes with Cox immigration and establish generic local identification of normalized structural parameters in two- and three-dimensional systems. An exact-equivalence Monte Carlo experiment demonstrates how third-order information can distinguish mechanisms with identical second-order structure, while revealing substantial finite-sample limitations under weak signals. For a restricted parametric family, we develop Whittle estimation from binned counts, establish consistency and asymptotic normality under appropriate identification conditions, and construct feasible sandwich standard errors accounting for estimated mean intensities. Simulations assess structural recovery and inference accuracy. An application to cryptocurrency transactions illustrates the sensitivity of inferred excitation to model specification and the limitations of structural interpretation based on spectral fit alone.

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Topics: Spurious relationship, Consistency (knowledge bases), Identification (biology), Parametric statistics, Event (particle physics), Mathematics

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