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

A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular $\mathbb{Z}^d$-actions