周期图的缺陷：准周期振荡分析中的非平稳性偏差
Pitfalls of periodograms: The non-stationarity bias in the analysis of quasi-periodic oscillations
摘要：
准周期振荡（Quasi-periodic oscillations，QPO）是理解天体在伽马射线暴、太阳耀斑和磁星耀斑等瞬变事件中动力学行为的一把重要钥匙。QPO的估计通常使用时间序列的周期图，并使用Whittle似然函数进行谱密度估计。然而，Whittle似然仅在时间序列是平稳的情况下有效，因为频率仓在其他情况下在统计上不是独立的。我们发现，如果时间序列是非平稳的，QPO的意义可以高度高估和估计的中心频率和QPO宽度可以过度约束。如果QPO仅存在于时间序列的一小部分中，并且噪声水平在整个时间序列中变化，则会发生这种效应。例如，如果瞬态之前或之后的背景噪声包括在时间序列中，或者如果低频噪声分布在时间序列上强烈变化，则可能发生这种情况。我们确认存在这种偏见，在以前报道的结果从太阳耀斑数据，并表明，意义可能被高度夸大。最后，我们提供了一些建议，帮助确定分析是否受到这种偏见的影响。
英文摘要：
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.
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