A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤd-actions
- 28 March 2018
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 55 (1) , 179-195
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.Keywords
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