The chi-square periodogram (CSP), developed over 40 years ago, continues to be one of the most popular methods to estimate the period of circadian (circa 24-h) rhythms. Previous work has indicated the CSP is sometimes less accurate than other methods, but understanding of why and under what conditions remains incomplete. Using simulated rhythmic time-courses, we found that the CSP is prone to underestimating the period in a manner that depends on the true period and the length of the time-course. This underestimation bias is most severe in short time-courses (e.g., 3 days), but is also visible in longer simulated time-courses (e.g., 12 days) and in experimental time-courses of mouse wheel-running and ex vivo bioluminescence. We traced the source of the bias to discontinuities in the periodogram that are related to the number of time-points the CSP uses to calculate the observed variance for a given test period. By revising the calculation to avoid discontinuities, we developed a new version, the greedy CSP, that shows reduced bias and improved accuracy. Nonetheless, even the greedy CSP tended to be less accurate on our simulated time-courses than an alternative method, namely the Lomb-Scargle periodogram. Thus, although our study describes a major improvement to a classic method, it also suggests that users should generally avoid the CSP when estimating the period of biological rhythms.

卡巴斯基周期图（CSP）开发于40年前，仍然是估计昼夜节律周期（大约24小时）的最流行方法之一。先前的工作表明，CSP有时不如其他方法准确，但是对为什么以及在什么条件下的理解仍然不完整。使用模拟的有节奏的时程，我们发现CSP倾向于以依赖于真实时长和时程长度的方式低估周期。这种低估偏差在较短的时间段（例如3天）中最为严重，但在较长的模拟时间段（例如12天）以及鼠标滚轮运行和离体生物发光的实验时间段中也很明显。我们在周期图中跟踪了偏差的来源，该偏差与CSP用于计算给定测试期间观察到的方差的时间点数量有关。通过修改计算以避免不连续性，我们开发了新版本贪婪的CSP，该版本可减少偏差并提高准确性。但是，即使是贪婪的CSP在我们模拟的时间过程中也趋向于比另一种方法（即Lomb-Scargle周期图）更不准确。因此，尽管我们的研究描述了对经典方法的重大改进，但它也建议用户在估算生物节律周期时通常应避免使用CSP。可以减少偏差并提高准确性。但是，即使是贪婪的CSP在我们模拟的时间过程中也趋向于比另一种方法（即Lomb-Scargle周期图）更不准确。因此，尽管我们的研究描述了对经典方法的重大改进，但它也建议用户在估算生物节律周期时通常应避免使用CSP。可以减少偏差并提高准确性。但是，即使是贪婪的CSP在我们模拟的时间过程中也趋向于比另一种方法（即Lomb-Scargle周期图）更不准确。因此，尽管我们的研究描述了对经典方法的重大改进，但它也建议用户在估算生物节律周期时通常应避免使用CSP。