Statistics of Extremes: Animation 3

An animation from the 2015 review by A.C. Davison and R. Huser, "Statistics of Extremes," from the Annual Review of Statistics and Its Application.

Illustration of extremal clustering for data simulated from an ARMAX(a) process with a ≥ 0, i.e., Y_j = max(aY _j−1, Z_j ), j = 1, 2, . . . , where the Z_j are independent unit Frechet random variables. The extremal index for this process is θ = max(1, a)/(1 + a), so extreme events form clusters with mean size 2 when a = 1. The value of a increases from a = 0 to a = 4 throughout the animation.