Maximum-likelihood estimators and random walks in long memory models

Abstract

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

Keywords:

• fractional Brownian motion
• maximum-likelihood estimation
• rosenblatt process
• random walk

2000 AMS Classification :

• 60G18
• 62M99

Acknowledgements

This work has been partially supported by the Laboratory ANESTOC PBCT ACT-13. Karine Bertin has been partially supported by the Project FONDECYT 1090285. Soledad Torres has been partially supported by the Project FONDECYT 1070919.

Additional information

Notes on contributors

Ciprian A. Tudor

Present address: Laboratoire Paul Painlevé Université de Lille 1 F-59655 Villeneuve d'Ascq France.