Aggregation of isotropic autoregressive fields

TL;DR

This paper examines how aggregating isotropic autoregressive models with random coefficients on a lattice can lead to fields exhibiting either short or long memory, depending on the distribution of the coefficients.

Contribution

It provides a detailed spectral density analysis of aggregated isotropic autoregressive fields with random coefficients, highlighting conditions for short and long memory behaviors.

Findings

Aggregated fields can exhibit either short or long memory.

Spectral density depends on the distribution of AR coefficients.

Long memory arises under specific coefficient law conditions.

Abstract

This note constitutes a corrigendum to the article of Azomahou, JSPI, 139:2581-2597. The aggregation of isotropic four nearest neighbors autoregressive models on the lattice, with random coefficient, is investigated. The spectral density of the resulting random field is studied in details for a large class of law of the AR coefficient. Depending on this law, the aggregated field may exhibit short memory or isotropic long memory.