Journal Article

Multitaper Magnitude‐Squared Coherence for Time Series With Missing Data: Understanding Oscillatory Processes Traced by Multiple Observables

Dodson‐Robinson, Sarah E., Haley, Charlotte

2025

Overview

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 α$\\alpha $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. Plain Language Summary The magnitude‐squared coherence (MSC) statistic detects oscillations with the same origin that show up in different types of measurements. For example, daily measurements of the air temperature at noon and the number of visitors to an outdoor swimming pool would likely have high MSC at a period of 1 year. This paper demonstrates how to apply a recently developed multitaper technique for estimating MSC between series of measurements that have some missing values. Our demonstration series are (a) the sun's brightness at a particular wavelength of ultraviolet light and (b) the disturbance of an equatorial ring of current in Earth's magnetosphere. MSC estimates show that both series trace solar oscillations with periods between 50 days and 5 years. Because of its superior statistical properties, we recommend that the multitaper method demonstrated here be widely adopted for analysis of heliospheric measurement series. Key Points Haley (2021, https://doi.org/10.1109/LSP.2021.3105926) extended the multitaper method for estimating magnitude‐squared coherence (MSC) to accommodate time series with missing data We demonstrate missing‐data multitaper MSC by showing that solar Lyman α flux and Dst index jointly trace known solar midterm oscillations We suggest that multitaper should be the preferred frequency domain method for heliospheric applications due to its superior performance

• Publisher: John Wiley & Sons, Inc,American Geophysical Union (AGU) - Wiley,American Geophysical Union (AGU)
• Subject: Astro-statistics techniques / bivariate / Estimates / Fourier analysis / Fourier transforms / frequency domain / Hypothesis testing / Irregular cadence / Lomb-Scargle periodogram / Missing data / multitaper / Period search / Solar physics / statistical techniques / Time series / Time series analysis