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

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

2006-06-08

arxiv.org/abs/math/0606200v2

Mathematics

Probability

Scientific paper

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.

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