Paper: arXiv 2610.19428

Authors: Jiwon Jung, Kiseop Lee

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical treatment of Hawkes processes, focusing on identification issues with latent common signals. It combines rigorous theoretical derivations with empirical validation through simulations and a real-world application, demonstrating a strong balance between advanced theory and practical relevance. The novelty lies in the use of third-order cumulants for identification and the detailed analysis of second-order non-identification.

Research Flowchart

  flowchart TD
    A[Research Goal: Identify and Mitigate Non-Identification in Multivariate Hawkes Processes] --> B{Key Methodology: Characterize Spurious Excitation, Develop Identification Criteria};
    B --> C{Data/Inputs: Synthetic Hawkes Data, Cryptocurrency Transaction Data};
    C --> D{Computational Processes: Second-Order Analysis, Third-Order Cumulant Derivation, Whittle Estimation, Monte Carlo Experiments};
    D --> E[Key Findings/Outcomes: Second-order Non-identification Proven, Third-order Identification for Normalized Parameters, Whittle Estimator Properties, Sensitivity of Cryptocurrency Inferences];