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Quasi-periodic oscillations (QPOs) are an important key to understand thedynamic behavior of astrophysical objects during transient events likegamma-ray bursts, solar flares, and magnetar flares. Searches for QPOs oftenuse the periodogram of the time series and perform spectral density estimationusing a Whittle likelihood function. However, the Whittle likelihood is onlyvalid if the time series is stationary since the frequency bins are otherwisenot statistically independent. We show that if time series are non-stationary,the significance of QPOs can be highly overestimated and estimates of thecentral frequencies and QPO widths can be overconstrained. The effect occurs ifthe QPO is only present for a fraction of the time series and the noise levelis varying throughout the time series. This can occur for example if backgroundnoise from before or after the transient is included in the time series or ifthe low-frequency noise profile varies strongly over the time series. Weconfirm the presence of this bias in previously reported results from solarflare data and show that significance can be highly overstated. Finally, weprovide some suggestions that help identify if an analysis is affected by thisbias.

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