Maximum likelihood estimators and random walks in long memory models

Karine Bertin (1) , Soledad Torres (1) , Ciprian A. Tudor (2, 3)

1 Departamento de Estadistica [Valparaiso]
2 CES - Centre d'économie de la Sorbonne
3 SAMOS - Statistique Appliquée et MOdélisation Stochastique

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random walks of the driving noise. We study the asymptotic behavior of the estimators and we give some numerical simulations to illustrate our results.

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

Karine Bertin, Soledad Torres, Ciprian A. Tudor. Maximum likelihood estimators and random walks in long memory models. 2009. ⟨hal-00184942v2⟩