Approximate variances for tapered spectral estimates

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.

► New approximation of the asymptotic variance for the smoothed tapered periodogram.
► It removes a certain discontinuity in the usual formula.
► Exact calculations show that it is more accurate than the usual formula.