Pitfalls of Periodograms: The Nonstationarity Bias in the Analysis of Quasiperiodic Oscillations

Abstract

Abstract Quasiperiodic 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 nonstationary, 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. Thus, we highlight the importance of careful segment selection prior to the analysis. 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 whether an analysis is affected by this bias.