A 2-Dimensional Functional Central Limit Theorem for Non-stationary Dependent Random Fields

TL;DR

This paper establishes an elementary invariance principle for multi-dimensional Brownian sheets with non-stationary, dependent random fields, enabling new statistical tests for spatial and panel data models.

Contribution

It introduces a 2D functional central limit theorem applicable to non-stationary dependent random fields, expanding the theoretical framework beyond independence and stationarity.

Findings

Proves a new invariance principle for non-stationary dependent fields.

Applicable to unit-root tests in spatial and panel data models.

Extends classical results to multi-dimensional, dependent contexts.

Abstract

We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel data models.