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
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