We show that the asymptotic behavior of the normalized maxima of a stationary sequence satisfying a weak distributional mixing and bivariate condition is completely determined by the marginal distribution of the process. Sufficient conditions are given in order for the maxima and minima to be asymptotically independent. An example of a 1-dependent sequence where the maxima and minima are not asymptotically independent is also provided.
"Maxima and Minima of Stationary Sequences." Ann. Probab. 7 (3) 453 - 460, June, 1979. https://doi.org/10.1214/aop/1176995046