  Based on the ratio of two block maxima, we propose a large sample test for
the length of memory of a stationary symmetric $\alpha$-stable discrete
parameter random field. We show that the power function converges to one as the
sample-size increases to infinity under various classes of alternatives having
longer memory in the sense of Samorodnitsky(2004). Ergodic theory of
nonsingular $\mathbb{Z}^d$-actions play a very important role in the design and
analysis of our large sample test.
