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

  • Ayan Bhattacharya (a1) and Parthanil Roy (a2)


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.


Corresponding author

* Postal address: Stochastics group, CWI, Amsterdam, North Holland, 1098XG, Netherlands. Email address:
** Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, RVCE Post, Bangalore, 560059, India.


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

  • Ayan Bhattacharya (a1) and Parthanil Roy (a2)


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