Fast calibration of weak FARIMA models

Samir Ben Hariz (1, 2) , Alexandre Brouste (2, 1) , Youssef Esstafa (2, 1) , Marius Soltane (3)

1 LMM - Laboratoire Manceau de Mathématiques
2 UM - Le Mans Université
3 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the onestep estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.

Mots clés: Weak FARIMA models; Le Cam's one-step estimator; Least squares estimator; Consistency; Asymptotic Normality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Samir Ben Hariz, Alexandre Brouste, Youssef Esstafa, Marius Soltane. Fast calibration of weak FARIMA models. ESAIM: Probability and Statistics, 2023, 27, pp.156-173. ⟨10.1051/ps/2022021⟩. ⟨hal-03700112⟩