多变量平稳Hawkes过程的谱分析
Spectral analysis of multivariate stationary Hawkes processes
AI总结：
本文研究了平稳多变量Hawkes过程的频域推断渐近有效性，通过构建聚类表示的减少累积度量上界，证明了函数中心极限定理，并在平稳性条件下证明了Whittle估计量的一致性，适用于具有厚尾互激发核的Hawkes过程。
摘要：
我们建立了平稳多变量Hawkes过程频域推断的渐近有效性，基于聚类表示的Hawkes过程的减少累积度量上界，证明了函数中心极限定理，并由此在平稳性条件下（即相互作用矩阵的谱半径ρ(ν)<1）证明了Whittle估计量的一致性，适用于具有厚尾互激发核的Hawkes过程。在较弱的额外矩条件下，我们进一步获得了渐近正态性，其极限协方差以二阶和四阶累积谱密度显式表示。我们还提出了一种简单的频域方法来检测多变量Hawkes过程子过程的联合独立性。通过模拟研究展示了Whittle估计量和独立性检验的性能。
英文摘要：
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant measures from the cluster representation of the Hawkes processes, we prove a functional central limit theorem and, as a consequence, consistency of the Whittle estimator under stationarity alone (i.e., the spectral radius of the interactions matrix $ρ(\boldsymbolν)<1$), applicable to Hawkes processes with heavy-tailed mutual-excitation kernels. Under mild extra moment conditions, we further obtain asymptotic normality with an explicit limiting covariance in terms of second- and fourth-order cumulant spectral densities. We also propose a simple frequency-domain method to detect joint independence of subprocesses of a multivariate Hawkes process. The performance of the Whittle estimator and the test of independence are demonstrated via simulation studies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
