With respect to the first example in Schimmel (2001), Van Dongen et al. (2001) conclude from their Lomb-Scargle analysis that the noise I used ‘contains new periodicities that are added to the signal (these periodicities by themselves resemble a harmonic series of a 38-hour rhythm).’ They infer that ‘the variance of the added noise is about five times as large as the variance of the signal’ causing the detection of the new significant periodicities in the noise prior to the 24-h bimodal rhythm. Moreover the ‘example reflects a combination of an extremely non-sinusoidal signal with noise that is not independent, which results in a time series that is difficult to analyze with virtually any known method.’ In the following, I briefly examine these concerns to avoid misunderstandings and to alert that with an inadequate use of the statistical significance test, misleading conclusions can be obtained. Although this paper further emphasizes difficulties in the detection with Lomb-Scargle periodograms, this should not be used as de-motivation. As stated in Schimmel (2001) Lomb-Scargle is a powerful technique but such as any other method one should be aware about its limitations, and use additional tools to constrain the true data characteristics.

中文翻译：

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随机噪声中的显着特征问题

关于 Schimmel (2001) 中的第一个例子，Van Dongen 等人。(2001) 从他们的 Lomb-Scargle 分析得出结论，我使用的噪声“包含添加到信号中的新周期性（这些周期性本身类似于 38 小时节奏的谐波系列）。” 他们推断“添加噪声的方差大约是信号方差的五倍”，从而导致在 24 小时双峰节律之前检测到噪声中新的显着周期性。此外，“示例反映了极非正弦信号与非独立噪声的组合，这导致了几乎任何已知方法都难以分析的时间序列”。在下面的，我简要地研究了这些问题以避免误解，并提醒注意，如果统计显着性检验使用不当，可能会得出误导性的结论。尽管本文进一步强调了 Lomb-Scargle 周期图检测的困难，但这不应被用作去动机。正如 Schimmel (2001) 所述，Lomb-Scargle 是一种强大的技术，但与任何其他方法一样，应该意识到其局限性，并使用其他工具来限制真实的数据特征。