We consider multivariate stationary processes $({\mathit{X}}_t)$ satisfying a stochastic recurrence equation of the form ${\mathit{X}}_t={𝕄}_t{\mathit{X}}_{t-1}+{\mathit{Q}}_t$, where $({\mathit{Q}}_t)$ are i.i.d. random vectors and ${𝕄}_t=\text{Diag}(b_1+c_1{M}_t,\text{…},b_d+c_d{M}_t)$ are i.i.d. diagonal matrices and (M_t) are i.i.d. random variables. We obtain a full characterization of the vector scaling regular variation properties of $({\mathit{X}}_t)$, proving that some coordinates X_t, i and X_t, j are asymptotically independent even though all coordinates rely on the same random input (M_t). We prove the asynchrony of extreme clusters among marginals with different tail indices. Our results are applied to some multivariate autoregressive conditional heteroskedastic (BEKK-ARCH and CCC-GARCH) processes and to log-returns. Angular measure inference shows evidences of asymptotic independence among marginals of diagonal SRE with different tail indices.

中文翻译：

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渐近独立 ex machina：对角 SRE 模型的极值理论

我们考虑多元平稳过程$({\mathit{X}}_{吨})$满足形式的随机递推方程${\mathit{X}}_{吨}={𝕄}_{吨}{\mathit{X}}_{吨-1}+{\mathit{问}}_{吨}$， 在哪里$({\mathit{问}}_{吨})$是 iid 随机向量和${𝕄}_{吨}=\text{诊断}(b_1+C_1{米}_{吨},\text{…},b_d+C_d{米}_{吨})$是 iid 对角矩阵， ( M _t ) 是 iid 随机变量。我们获得了向量缩放规则变化特性的完整表征$({\mathit{X}}_{吨})$，证明了一些坐标X _{t ,  i}和X _{t ,  j}是渐近独立的，即使所有坐标都依赖于相同的随机输入 ( M _t )。我们证明了具有不同尾指数的边缘之间的极端集群的异步性。我们的结果应用于一些多元自回归条件异方差（BEKK-ARCH 和 CCC-GARCH）过程和对数返回。角度测量推断显示了具有不同尾指数的对角 SRE 的边缘之间渐近独立的证据。