Pitfalls of periodograms: The non-stationarity bias in the analysis of quasi-periodic oscillations

TL;DR

This paper highlights how non-stationarity in time series can lead to overestimating the significance of quasi-periodic oscillations when using periodograms, especially in transient astrophysical events.

Contribution

It demonstrates the bias introduced by non-stationarity in QPO analysis and offers methods to identify when this bias affects results.

Findings

Non-stationarity causes overestimation of QPO significance.

Bias occurs when QPOs are only present temporarily or noise varies.

Previously reported QPO significances may be overstated due to this bias.

Abstract

Quasi-periodic oscillations (QPOs) are an important key to understand the dynamic behavior of astrophysical objects during transient events like gamma-ray bursts, solar flares, and magnetar flares. Searches for QPOs often use the periodogram of the time series and perform spectral density estimation using a Whittle likelihood function. However, the Whittle likelihood is only valid if the time series is stationary since the frequency bins are otherwise not statistically independent. We show that if time series are non-stationary, the significance of QPOs can be highly overestimated and estimates of the central frequencies and QPO widths can be overconstrained. The effect occurs if the QPO is only present for a fraction of the time series and the noise level is varying throughout the time series. This can occur for example if background noise from before or after the transient is included in the time series or if the low-frequency noise profile varies strongly over the time series. We confirm the presence of this bias in previously reported results from solar flare data and show that significance can be highly overstated. Finally, we provide some suggestions that help identify if an analysis is affected by this bias.