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

French

Les modèles de Hawkes multivariés sont largement utilisés pour mesurer les interactions endogènes dans les données d'événement, mais les signaux communs latents peuvent générer une excitation apparente même sans interaction structurelle. Nous caractérisons la projection linéaire résultante et construisons des processus de Hawkes stables, non négatifs qui partagent l'intensité moyenne et le spectre de Bartlett des modèles de signaux communs en dépit d'avoir des mécanismes d'excitation différents. Cela établit une forme concrète de non-identification de deuxième ordre. Nous dérivons des cumulations de troisième ordre intégrées pour les processus de Hawkes avec l'immigration de Cox et établissons une identification locale générale des param

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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