A class of first-order autoregressive processes is given for which the extreme value limit theorems of Loynes and Leadbetter do not apply. A limit theorem is derived for these processes that depends on the parameter $r$, an integer greater than or equal to 2.
"A Limit Theorem for the Maximum of Autoregressive Processes with Uniform Marginal Distributions." Ann. Probab. 9 (1) 145 - 149, February, 1981. https://doi.org/10.1214/aop/1176994514