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

Ayan Bhattacharya; Parthanil Roy

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arXiv · 1611.08874

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

Ayan Bhattacharya·Parthanil Roy

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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.

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Ayan Bhattacharya, Parthanil Roy. 2016-11-27. A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular $\mathbb{Z}^d$-actions. https://arxiv.org/abs/1611.08874

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