Approximate variances for tapered spectral estimates

TL;DR

This paper introduces an improved approximation for the asymptotic variance of tapered spectral estimates, enhancing accuracy over traditional formulas by accounting for covariance between frequencies.

Contribution

It presents a novel approximation method for the variance of tapered spectral estimates that reduces discontinuities and improves accuracy compared to existing formulas.

Findings

The approximation outperforms the traditional formula in Gaussian white noise scenarios.

It provides more accurate variance estimates for AR(4) processes.

The method effectively removes discontinuities in variance calculations.

Abstract

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.