Limiting distribution of the least squares<br />estimates in polynomial regression with long<br />memory noises

HAL Id: halshs-00409571

https://halshs.archives-ouvertes.fr/halshs-00409571

Preprint submitted on 10 Aug 2009

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Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises

Mohamed Boutahar

To cite this version:

Mohamed Boutahar. Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises. 2006. �halshs-00409571�

GREQAM

Universités d'Aix-Marseille II et III

Document de Travail

n°2006-01

Limiting distribution of the least squares estimates in polynomial regression with long

memory noises

Mohamed BOUTAHAR

January 2006

Résumé :

We give the limiting distribution of the least squares estimator in the polynomial regression model driven by some long memory processes. We prove that with an appropriate

normalization, the estimation error converges, in distribution, to a random vector which components are a mixture of stochastic integrals. These integrals are with respect to a Lebesgue measure, and can be computed recursively where the seed is a random variable which depends on the assumptions made on the noise process. The limiting distribution can be Gaussian or non Gaussian.

Keywords: Fractional Brownian motion; Long memory; Multiple Wiener-Itô integral;

Polynomial regression; Stochastic integral