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

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.

19 pages, 11 Figures

References in corpus (18)

• Bayesian inference for compact binary coalescences with BILBY: Validation and application to the first LIGO--Virgo gravitational-wave transient catalogue
• A review of quasi-periodic oscillations from black hole X-ray binaries: observation and theory
• Quasi-periodic pulsations in solar and stellar flares: an overview of recent results
• Coherent WaveBurst, a pipeline for unmodeled gravitational-wave data analysis
• A large-scale search for evidence of quasi-periodic pulsations in solar flares
• Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra
• Persistent Quasi-Periodic Pulsations During a Large X-Class Solar Flare
• Statistical Study of GOES X-ray Quasi-Periodic Pulsations in Solar Flares
• Quasi-Periodic Oscillations in Short Recurring Bursts of the Soft-Gamma Repeater J1550-5418
• Coronal Fourier power spectra: implications for coronal seismology and coronal heating
• A blueprint of state-of-the-art techniques for detecting quasi-periodic pulsations in solar and stellar flares
• Looking at Blazar Light Curve Periodicities with Gaussian Processes
• A Comprehensive Power Spectral Density Analysis of Astronomical Time Series. II. The Swift/BAT Long Gamma-Ray Bursts
• Toward the unambiguous identification of supermassive binary black holes through Bayesian inference
• Intermittency and Lifetime of the 625 Hz QPO in the 2004 Hyperflare from the Magnetar SGR 1806-20 as evidence for magnetic coupling between the crust and the core
• Detection of Very Low-Frequency Quasi-Periodic Oscillations in the 2015 Outburst of V404 Cygni
• Fitting FFT-derived Spectra: Theory, Tool, and Application to Solar Radio Spike Decomposition
• Detection of Millihertz Quasi-Periodic Oscillations in the X-Ray Binary 1RXS J180408.9$-$342058

Cited by in corpus (11)

• Kilohertz quasiperiodic oscillations in short gamma-ray bursts
• The Peculiar Precursor of a Gamma-Ray Burst from a Binary Merger Involving a Magnetar
• Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes
• Search for Quasi-Periodical Oscillations in Precursors of Short and Long Gamma Ray Bursts
• Prevalence of non-stationarity in quasi-periodic pulsations (QPPs) associated with M- and X-class solar flares
• Evidence for a brief appearance of gamma-ray periodicity after a compact star merger
• Quasi-Periodic Peak Energy Oscillations in X-ray Bursts from SGR J1935+2154
• Searching for Quasi-Periodic Eruptions using Machine Learning
• Searching for quasi-periodicities in short transients: the curious case of GRB 230307A
• A search for periodic activity in multi-peaked long gamma-ray bursts
• X-ray Quasi-Periodic Oscillations in Active Galactic Nuclei and Their Implications for the Changing Look Phenomenon