  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.
