The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes, but not yet studied for additive linear processes. In this article, we fill this gap by verifying the tail adversarial stability condition for regularly varying additive linear processes. We in addition consider extensions of the result to a stochastic volatility generalization and to a max-linear counterpart. We also address the invariance of tail adversarial stability under monotone transforms. Some implications for limit theorems in statistical context are also discussed.

翻译：尾部对抗稳定性概念已被证明在获得尾部依赖时间序列的极限定理方面具有实用性。与经典强混合框架相比，其含义和优势已在最大线性过程中得到检验，但尚未针对加性线性过程进行研究。本文通过验证正则变化加性线性过程的尾部对抗稳定性条件，填补了这一空白。此外，我们考虑了该结果向随机波动率推广及最大线性对应过程的扩展，并探讨了尾部对抗稳定性在单调变换下的不变性。同时，还讨论了其在统计背景下极限定理中的若干含义。