Estimation of the asymptotic variance matrix of the least squares estimator of weak FARIMA models

In this article, we propose a consistent estimator for the asymptotic variance matrix of the least squares estimator in Fractionally AutoRegressive Integrated Moving‐Average (FARIMA) models. Our approach allows for error terms that are uncorrelated, but not necessarily independent. Modified versions of the Wald, Lagrange Multiplier, and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters of these models, particularly for assessing the presence or absence of long‐memory characteristics. Simulation studies are conducted to support the theoretical findings. Additionally, an application to Nikkei stock returns and monthly temperature data demonstrates the practical relevance of the theoretical results.