Tail Adversarial Stability for Regularly Varying Linear Processes and their Extensions

The recently introduced notion of tail adversarial stability has been proven useful in studying tail dependent time series and obtaining their limit theorems. 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 that have also been commonly used in modeling extremal clusters and tail dependence in time series. In this article, we fill this gap by verifying the tail adversarial stability condition for regularly varying additive linear processes. A comparison with the classical strong mixing condition is also given in the context of tail autocorrelation estimation. We in addition consider extensions of the result on an additive linear process to its stochastic volatility generalization and to its max-linear counterpart. Some implications for limit theorems in statistical context are also discussed.