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

Abstract

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.

Accepted for publication in Journal of Applied Probability

References in corpus (1)

• Maximal Moments and Uniform Modulus of Continuity for Stable Random Fields