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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.
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This content will become publicly available on June 1, 2026
Multitaper Magnitude‐Squared Coherence for Time Series With Missing Data: Understanding Oscillatory Processes Traced by Multiple Observables
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.
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- Award ID(s):
- 2307978
- PAR ID:
- 10625827
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Earth and Space Science
- Volume:
- 12
- Issue:
- 6
- ISSN:
- 2333-5084
- Subject(s) / Keyword(s):
- spectral analysis missing data solar midterm periodicities
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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