  We propose an approximation of the asymptotic variance that removes a certain
discontinuity in the usual formula for the raw and the smoothed periodogram in
case a data taper is used. It is based on an approximation of the covariance of
the (tapered) periodogram at two arbitrary frequencies. Exact computations of
the variances for a Gaussian white noise and an AR(4) process show that the
approximation is more accurate than the usual formula.
