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.
Categories: math.PR