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While the Lomb-Scargle periodogram is foundational to astronomy, it has asignificant shortcoming: the variance in the estimated power spectrum does notdecrease as more data are acquired. Statisticians have a 60-year history ofdeveloping variance-suppressing power spectrum estimators, but most are notused in astronomy because they are formulated for time series with uniformobserving cadence and without seasonal or daily gaps. Here we demonstrate howto apply the missing-data multitaper power spectrum estimator to spacecraftdata with uniform time intervals between observations but missing data duringthruster fires or momentum dumps. The F-test for harmonic components may beapplied to multitaper power spectrum estimates to identify statisticallysignificant oscillations that would not rise above a white noise-based falsealarm probability. Multitapering improves the dynamic range of the powerspectrum estimate and suppresses spectral window artifacts. We show that themultitaper - F-test combination applied to Kepler observations of KIC 6102338detects differential rotation without requiring iterative sinusoid fitting andsubtraction. Significant signals reside at harmonics of both fundamentalrotation frequencies and suggest an antisolar rotation profile. Next we use themissing-data multitaper power spectrum estimator to identify the oscillationmodes responsible for the complex "scallop shell" shape of the K2 light curveof EPIC 203354381. We argue that multitaper power spectrum estimators should beused for all time series with regular observing cadence.

Optimal frequency-domain analysis for spacecraft time series: Introducing the missing-data multitaper power spectrum estimator