A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular Zd-actions

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