Identification d'un processus autorégressif gaussien stable par la méthode de moyennisation logarithmique

Faouzi Chaabane (1) , Hamdi Fathallah (2)

1 EASMS - Equipe d'Analyse Stochastique et Modélisation Statistique
2 LMV - Laboratoire de Mathématiques de Versailles

In the present work, we consider a stable one-dimensional gaussian autoregressive model in continous time. Using the limit theorems with logarithmic averaging obtained for continous local martingales, we construct then an estimator of the noise covariance $\sigma^{2}$ and an estimator of $\theta$ different of the one of the least squares estimator. By exploiting the weighting method we ameliorate the convergence rates of these new estimators.

Mots clés: Martingale; Weight; Almost-sure central limit theorem; Logarithmic central limit theorem; law of iterated logarithm

Domaines: Probabilités [math.PR]

Faouzi Chaabane, Hamdi Fathallah. Identification d'un processus autorégressif gaussien stable par la méthode de moyennisation logarithmique. 2006. ⟨hal-00079076v2⟩