Multitaper magnitude-squared coherence for time series with missing data: Understanding oscillatory processes traced by multiple observables

TL;DR

This paper extends the multitaper method to estimate magnitude-squared coherence in time series with missing data, demonstrating its effectiveness in detecting solar oscillations and recommending its use for heliospheric datasets.

Contribution

The paper introduces an extension of the classical multitaper technique to handle missing data in time series with uniform cadence, improving coherence estimation accuracy.

Findings

Successfully detected solar mid-term oscillations in missing-data time series.

Demonstrated the superiority of multitaper over Welch's method in statistical properties.

Recommended multitaper methods for analyzing heliospheric time series with gaps.

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 datasets, 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 $\alpha$ 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.