Keywords: Power Spectrum, Multitaper, Missing Data, Bootstrap

Abstract: Multitapering is a technique designed to improve on the notorious periodogram estimate of the power spectrum. We indicate how to construct favorable collections of orthogonal tapers for time series observed with gaps, and show how to use statistical resampling techniques to calculate uncertainty estimates for multitaper estimates. We use simulated and actual solar acoustic oscillation datasets to illustrate the proposed methodology. We show the superiority of the resulting estimates by comparing them to alternative power spectrum estimates. The Global Oscillation Network Group, a state-of-the-art helioseismological experiment, recently adopted our procedure, and reported an increase in the number and in the precision of the estimated solar oscillation mode parameters.