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

Korean

멀티 바이너리 호크스 모델은 이벤트 데이터에서 내성 상호 작용을 측정하는 데 널리 사용되지만 잠재적 인 일반 신호는 구조적 상호 작용없이도 명백한 흥분을 생성 할 수 있습니다. 우리는 결과의 선형 투영을 특징으로하고 2 차원 및 3 차원 시스템에서 표준화 된 구조적 매개 변수의 일반적인 지역 식별을 구축하는 안정적이고 부정적인 호크스 프로세스를 구축합니다. 서로 다른 흥분 메커니즘이 있음에도 불구하고 보통 신호 모델의 Bartlett 스펙트럼을 측정합니다. 이것은 두 번째 계층의 식별이없는 구체적인 형태를 구축합니다. 우리는 코스 이민과 함께 호크스 프로세스에 대한 통합 된 제 3 계층 축적을

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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