Based on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to 1 as the sample-size increases to ∞ under various classes of alternatives having longer memory in the sense of Samorodnitsky (2004). Ergodic theory of nonsingular Zd-actions plays a very important role in the design and analysis of our large sample test.

extreme value theory, Long range dependence, nonsingular group action, stationary S?S random field, statistical hypothesis testing
dx.doi.org/10.1017/jpr.2018.12
Journal of Applied Probability

Bhattacharya, A, & Roy, P. (2018). A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular Zd-actions. Journal of Applied Probability, 55(1), 179–195. doi:10.1017/jpr.2018.12