This investigation establishes the theoretical and practical limits of Kolmogorov-Zurbenko periodograms with dynamic smoothing in their estimation of signal frequencies in terms of their sensitivity, accuracy, resolution, and robustness. While the DiRienzo-Zurbenko algorithm performs dynamic smoothing based on local variation in a periodogram, the Neagu-Zurbenko algorithm performs dynamic smoothing based on local departure from linearity in a periodogram. This article begins with a summary of the statistical foundations for both the DiRienzo-Zurbenko algorithm and the Neagu-Zurbenko algorithm, followed by instructions for accessing and utilizing these approaches within the R statistical program platform. Brief definitions, importance, statistical bases, theoretical and practical limits, and demonstrations are provided for their sensitivity, accuracy, resolution, and robustness in estimating signal frequencies. 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 these approaches are compared to the autoregressive integral moving average (ARIMA) approach, with support again garnered for their being robust when data is missing. Throughout, the article contrasts the limits of Kolmogorov-Zurbenko periodograms with dynamic smoothing to those of log-periodograms with static smoothing, while also comparing the performance of the DiRienzo-Zurbenko algorithm to that of the Neagu-Zurbenko algorithm. It concludes by delineating next steps to establish the precision with which Kolmogorov-Zurbenko periodograms with dynamic smoothing estimate signal strength.

翻译：本研究从灵敏度、精度、分辨率和鲁棒性四个方面，确立了动态平滑Kolmogorov-Zurbenko周期图在信号频率估计中的理论与实际极限。DiRienzo-Zurbenko算法基于周期图中的局部变异进行动态平滑，而Neagu-Zurbenko算法则基于周期图中的局部非线性偏离进行动态平滑。本文首先概述了DiRienzo-Zurbenko算法和Neagu-Zurbenko算法的统计学基础，随后提供了在R统计程序平台中访问和使用这些方法的指南。文章简要阐述了这两种方法在估计信号频率时的灵敏度、精度、分辨率和鲁棒性的定义、重要性、统计学基础、理论与实际极限，并进行了演示。接着，通过使用一个模拟时间序列——其中两个频率接近的信号嵌入在显著水平的随机噪声中——将这些方法的预测能力与自回归积分滑动平均（ARIMA）方法进行比较，结果再次支持了它们在数据缺失情况下的鲁棒性。全文将动态平滑Kolmogorov-Zurbenko周期图的极限与静态平滑对数周期图的极限进行了对比，同时也比较了DiRienzo-Zurbenko算法与Neagu-Zurbenko算法的性能。最后，文章通过概述后续步骤，明确了动态平滑Kolmogorov-Zurbenko周期图估计信号强度的精度范围。