Estimating FARIMA models with uncorrelated but non-independent error terms - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Estimating FARIMA models with uncorrelated but non-independent error terms

Résumé

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of fractionally integrated autoregressive moving-average (FARIMA) models under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. We relax considerably the independence and even the martingale difference assumptions on the innovation process to extend the range of application of the FARIMA models. We propose a consistent estimator of the asymptotic covariance matrix of the LSE which may be very different from that obtained in the standard framework. A self-normalized approach to confidence interval construction for weak FARIMA model parameters is also presented. All our results are done under a mixing assumption on the noise. Finally, some simulation studies and an application to the daily returns of stock market indices are presented to corroborate our theoretical work.
Fichier principal
Vignette du fichier
WeakFARIMA161220-SISP.pdf (788.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02316503 , version 1 (15-10-2019)
hal-02316503 , version 2 (10-03-2021)

Identifiants

Citer

Yacouba Boubacar Maïnassara, Youssef Esstafa, Bruno Saussereau. Estimating FARIMA models with uncorrelated but non-independent error terms. 2021. ⟨hal-02316503v2⟩
84 Consultations
132 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More