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A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions
Published online by Cambridge University Press: 28 March 2018
Abstract
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.
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- Copyright © Applied Probability Trust 2018
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