We show the consistency of the log-periodogram regression estimate of the long memory parameter for long range dependent linear, not necessarily Gaussian, time series when we make a pooling of periodogram ordinates. Then, we study the asymptotic behavior of the tapered periodogram of long range dependent time series for frequencies near the origin, and we obtain the asymptotic distribution of the log-periodogram estimate for possibly non-Gaussian observation when the tapered periodogram is used. For these results we rely on higher order asymptotic properties of a vector of periodogram ordinates of the linear innovations. Finally, we assess the validity of the asymptotic results for finite samples via Monte Carlo simulation.