动态平滑 Kolmogorov-Zurbenko 周期图在信号频率估计中的理论与实践极限
Theoretical and Practical Limits of Kolmogorov-Zurbenko Periodograms with Dynamic Smoothing in Estimating Signal Frequencies
AI总结：
本文评估两种动态平滑 Kolmogorov-Zurbenko 周期图算法的频率估计极限，并通过含噪、近频和缺失数据模拟与 ARIMA 及静态平滑方法比较。
摘要：
本研究从灵敏度、准确性、分辨率和鲁棒性方面，确立了采用动态平滑的 Kolmogorov-Zurbenko 周期图在估计信号频率时的理论与实践极限。DiRienzo-Zurbenko 算法基于周期图中的局部变化执行动态平滑，而 Neagu-Zurbenko 算法则基于周期图中对线性的局部偏离执行动态平滑。本文首先概述 DiRienzo-Zurbenko 算法和 Neagu-Zurbenko 算法的统计基础，随后说明如何在 R 统计程序平台中获取和使用这些方法。文中针对二者在估计信号频率时的灵敏度、准确性、分辨率和鲁棒性，给出了简要定义、重要性、统计依据、理论与实践极限以及演示。接着，利用一个将两个频率接近的信号嵌入显著随机噪声水平中的模拟时间序列，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，并再次获得证据支持其在数据缺失时具有鲁棒性。全文始终将采用动态平滑的 Kolmogorov-Zurbenko 周期图的极限与采用静态平滑的对数周期图的极限进行对比，同时比较 DiRienzo-Zurbenko 算法与 Neagu-Zurbenko 算法的性能。文章最后勾画了后续步骤，以确立采用动态平滑的 Kolmogorov-Zurbenko 周期图估计信号强度时的精度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
