Abstract
<jats:p>Earth scientists and exoplanet astronomers rely on spectral analysis of time series to study climate cycles and discover planets orbiting nearby stars. However, geological time series often have uneven timesteps due to nonuniform stratigraphic layer thickness, and exoplanet time series always have uneven timesteps with frequent interruptions due to daytime, poor weather, and telescope scheduling. The Thomson (1982) multitaper power spectrum estimator is the gold-standard spectral analysis tool for evenly spaced time series because it is optimally bandlimited and consistent. The Bronez (1988) multitaper power spectrum estimator for unevenly spaced data, which requires solving a generalized eigenvalue problem for every frequency in the grid, is usually considered too computationally expensive to be practical. We have implemented a multithreaded Julia version of the Bronez multitaper power spectrum estimator that can return results for a time series with N ~= 1000 data points on 10 processors in under one hour. Since no interpolation or approximation is used, the computed tapers are fully orthogonal. Our software includes the harmonic F-test for oscillatory components. We demonstrate the Bronez multitaper power spectrum estimator using two datasets: (1) South China Sea subsurface and mixed-layer temperature reconstructions spanning 2800 kyr and (2) line-of-sight velocity observations of the sunlike star HD 20794. The F-test recovers Earth's 41 kyr glacial cycle from (1) and planets HD 20794 b, c from (2). Code for the Bronez multitaper power spectrum estimator and harmonic F-test is available on GitHub.</jats:p>