This investigation establishes the theoretical and practical limits of the Kolmogorov-Zurbenko periodogram with DiRienzo-Zurbenko algorithm smoothing with respect to sensitivity (i.e., ability to detect weak signals), accuracy (i.e., ability to correctly identify signal frequencies), resolution (i.e., ability to separate signals with close frequencies), and robustness (i.e., sensitivity, accuracy, and resolution despite high levels of missing data). Compared to standard periodograms that utilize static smoothing with a fixed window width, Kolmogorov-Zurbenko periodograms with DiRienzo-Zurbenko algorithm smoothing utilize dynamic smoothing with a variable window width. This article begins with a summary of its statistical derivation and development followed by instructions for accessing and utilizing this approach within the R statistical program platform. Brief definitions, importance, statistical bases, theoretical and practical limits, and demonstrations are provided for its sensitivity, accuracy, resolution, and robustness. Next using a simulated time series in which two signals close in frequency are embedded in a significant level of random noise, the predictive power of this approach is compared to an autoregressive integral moving average (ARIMA), with support also garnered for its being robust even in the face of a high level of missing data. The article concludes with brief descriptions of studies across a range of scientific disciplines that have capitalized on the power of the Kolmogorov-Zurbenko periodogram with DiRienzo-Zurbenko algorithm smoothing.

翻译：本研究确立了Kolmogorov-Zurbenko周期图结合DiRienzo-Zurbenko算法平滑在灵敏度（即检测微弱信号的能力）、准确度（即正确识别信号频率的能力）、分辨率（即区分频率相近信号的能力）和鲁棒性（即在高缺失数据水平下仍保持灵敏度、准确度和分辨率的能力）方面的理论与实际极限。相较于采用固定窗宽静态平滑的标准周期图，结合DiRienzo-Zurbenko算法平滑的Kolmogorov-Zurbeno周期图采用可变窗宽的动态平滑方法。本文首先概述其统计推导与发展过程，随后说明如何在R统计程序平台中调用和使用该方法。针对其灵敏度、准确度、分辨率与鲁棒性，文章提供了简要定义、重要性说明、统计基础、理论及实际极限论证与示例演示。接着通过模拟时间序列（其中两个频率相近的信号嵌入显著水平的随机噪声），将该方法的预测能力与自回归积分滑动平均（ARIMA）模型进行比较，并证明其即使在数据大量缺失的情况下仍具有鲁棒性。文章最后简要介绍了多个科学领域利用Kolmogorov-Zurbenko周期图结合DiRienzo-Zurbenko算法平滑方法所开展的研究案例。