多变量Hawkes过程中的共同信号、虚假交叉激励与识别
Common Signals, Spurious Cross-Excitation, and Identification in Multivariate Hawkes Processes
AI总结：
该研究针对多变量Hawkes过程，分析了共同信号导致的虚假交叉激励问题，推导了相关累积量并建立参数识别性，开发了Whittle估计方法，通过模拟和加密货币交易应用验证了模型的有效性与局限性。
摘要：
多变量Hawkes模型被广泛用于度量事件数据中的内生交互作用，但潜在的共同信号即使在无结构交互的情况下也会产生明显的激励效应。我们对由此产生的线性投影进行了表征，并构建了稳定、非负的Hawkes过程，这些过程尽管具有不同的激励机制，却共享共同信号模型的平均强度和Bartlett谱，这确立了二阶非识别的具体形式。我们推导了带有Cox移民的Hawkes过程的三阶累积量积分，并在二维和三维系统中建立了归一化结构参数的通用局部识别性。一项精确等价的蒙特卡洛实验展示了三阶信息如何区分具有相同二阶结构的机制，同时揭示了弱信号下显著的有限样本局限性。对于受限参数族，我们从分箱计数中开发了Whittle估计，在适当的识别条件下建立了一致性和渐近正态性，并构建了可行的三明治标准误以考虑估计的平均强度。模拟评估了结构恢复和推断准确性，对加密货币交易的应用则说明了推断的激励对模型设定的敏感性，以及仅基于谱拟合的结构解释的局限性。
英文摘要：
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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