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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 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. 

Abstract Measured spectral shifts due to intrinsic stellar variability (e.g., pulsations, granulation) and activity (e.g., spots, plages) are the largest source of error for extreme-precision radial-velocity (EPRV) exoplanet detection. Several methods are designed to disentangle stellar signals from true center-of-mass shifts due to planets. The Extreme-precision Spectrograph (EXPRES) Stellar Signals Project (ESSP) presents a self-consistent comparison of 22 different methods tested on the same extreme-precision spectroscopic data from EXPRES. Methods derived new activity indicators, constructed models for mapping an indicator to the needed radial-velocity (RV) correction, or separated out shape- and shift-driven RV components. Since no ground truth is known when using real data, relative method performance is assessed using the total and nightly scatter of returned RVs and agreement between the results of different methods. Nearly all submitted methods return a lower RV rms than classic linear decorrelation, but no method is yet consistently reducing the RV rms to sub-meter-per-second levels. There is a concerning lack of agreement between the RVs returned by different methods. These results suggest that continued progress in this field necessitates increased interpretability of methods, high-cadence data to capture stellar signals at all timescales, and continued tests like the ESSP using consistent data sets with more advanced metrics for method performance. Future comparisons should make use of various well-characterized data sets—such as solar data or data with known injected planetary and/or stellar signals—to better understand method performance and whether planetary signals are preserved.