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Abstract To explore the hypothesis of a common source of variability in two time series, observers may estimate the magnitude‐squared coherence (MSC), which is a frequency‐domain view of the cross correlation. For time series that do not have uniform observing cadence, MSC can be estimated using Welch's overlapping segment averaging. However, multitaper has superior statistical properties to Welch's method in terms of the tradeoff between bias, variance, and bandwidth. The classical multitaper technique has recently been extended to accommodate time series with underlying uniform observing cadence from which some observations are missing. This situation is common for solar and geomagnetic data sets, which may have gaps due to breaks in satellite coverage, instrument downtime, or poor observing conditions. We demonstrate the scientific use of missing‐data multitaper magnitude‐squared coherence by detecting known solar mid‐term oscillations in simultaneous, missing‐data time series of solar Lyman flux and geomagnetic Disturbance Storm Time index. Due to their superior statistical properties, we recommend that multitaper methods be used for all heliospheric time series with underlying uniform observing cadence. 

Abstract GJ 1002 is reported to host two Earth-mass planets in the habitable zone. We applied frequency-domain techniques for validating planet discoveries to the ESPRESSO and CARMENES radial velocity (RV) and cross-correlation full width at half maximum time series. Siegel’s test applied to Welch’s power spectrum estimates suggests that periodicity in the RV time series may not be statistically significant. The frequency response to a sinusoid with the frequency of planet b, or pseudowindow, shows excess power near the frequency of planet c. Finally, a Monte Carlo experiment where we create new RV time series realizations by adding white noise to original data reveals that the highest periodogram peak sometimes occurs at half the frequency of planet c. More extreme-precision observations are required to confirm RV oscillations and constrain the rotation period. 

Abstract Based on radial velocities, EXORAP photometry, and activity indicators, the HArps-n red Dwarf Exoplanet Survey (HADES) team reported a 16.3 days rotation period for the M dwarf GJ 3942. However, an estimate of the magnitude-squared coherence between the HADES RV and Hαtime series has significant peaks at frequencies 1/16 day⁻¹and 1/32 day⁻¹. We turn to TESS photometry to test the hypothesis that the true rotation period is 32 days with 16 days harmonic. Although the average TESS periodogram has peaks at harmonics of 1/16 day⁻¹, the harmonic sequence is not fully resolved according to the Rayleigh criterion. The TESS observations suggest a 1/16 day⁻¹rotation frequency and a 1/32 day⁻¹subharmonic, though resolution makes the TESS rotation detection ambiguous. 

Abstract While the Lomb–Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60 yr history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. TheF-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise–based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper–F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex “scallop-shell” shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.