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The notion of tail adversarial stability has been proven useful in obtaininglimit theorems for tail dependent time series. Its implication and advantageover the classical strong mixing framework has been examined for max-linearprocesses, but not yet studied for additive linear processes. In this article,we fill this gap by verifying the tail adversarial stability condition forregularly varying additive linear processes. We in addition consider extensionsof the result to a stochastic volatility generalization and to a max-linearcounterpart. We also address the invariance of tail adversarial stability undermonotone transforms. Some implications for limit theorems in statisticalcontext are also discussed.

Tail Adversarial Stability for Regularly Varying Linear Processes and their Extensions