This paper considers the statistical inference for stationary time series under weak assumptions. Firstly, a frequency domain approach is proposed for fast estimation based on a one step procedure. This method correct an initial Whittle guess estimator on a subsample by a single Fisher scoring step. The resulting estimator shares the same asymptotic properties of the Whittle estimator on the whole sample and reduce drastically the computation time. Secondly, the asymptotic covariance matrix of the Whittle estimator is estimated for full inference solving an open question raised by Shao, X. (2010).