The V/S test of long-range dependence in random fields

TL;DR

This paper extends the V/S test for long-range dependence from sequences to random fields, allowing for non-isotropic dependence and evaluating its power through simulations.

Contribution

It generalizes the V/S test to random fields without assuming isotropy, broadening its applicability for detecting long memory in spatial data.

Findings

The generalized V/S test effectively detects long-range dependence in random fields.

Simulation results demonstrate the test's power varies with different types of long memory.

The method does not require isotropy assumptions, unlike previous approaches.

Abstract

Recently, Giraitis et al. (2003, [10]) proposed the $V/S$ statistic for testing long memory in random sequences. We generalize this statistic to the setting of random fields. The null hypothesis is concerned with short memory random fields while the alternative contains a very large family of long memory random fields. Contrary to most of the previous works dealing with long-range dependence, no assumption is made about the isotropy of the strong dependence. Some simulations are presented in order to assess the power of the test according to the kind of long memory in presence.