  In this paper, we investigate the asymptotic properties of Le Cam's one-step
estimator for weak Fractionally AutoRegressive Integrated Moving-Average
(FARIMA) models. For these models, noises are uncorrelated but neither
necessarily independent nor martingale differences errors. We show under some
regularity assumptions that the one-step estimator is strongly consistent and
asymptotically normal with the same asymptotic variance as the least squares
estimator. We show through simulations that the proposed estimator reduces
computational time compared with the least squares estimator. An application
for providing remotely computed indicators for time series is proposed.
