估计时间序列的执行摘要：趋势
Estimating an Executive Summary of a Time Series: The Tendency
AI总结：
本文基于内蕴时间分解（ITD）和信息论分析，提出两种从ITD基线中选择时间序列趋势的方法，并证明其在多尺度信号中的可解释性与计算鲁棒性优于传统低通滤波方案。
摘要：
本文重新审视了将信号分解为趋势和残差的问题。趋势描述了信号的执行摘要，它概括了信号的显著特征，同时忽略了看似随机且不太重要的方面。基于内蕴时间分解（ITD）和信息论分析，我们提出了两种替代程序来从ITD基线中选择趋势。第一种基于最大极值突出度，即每个基线内极值之间的最大差值。具体而言，该方法选择趋势的依据是：从该基线进行一次ITD步骤将导致最大突出度出现最大幅度的下降。第二种方法使用ITD中的旋转，并将趋势选择为相关旋转在统计上平稳的最后一条基线。我们深入比较了所提方法获得的趋势与通过传统低通滤波方案（特别是Hodrik-Prescott（HP）滤波器）获得的趋势在信息内容和可解释性方面的差异。我们的研究结果强调了这些趋势在性质和可解释性上的根本区别，突出了它们依赖于上下文的实用性，并重点关注多尺度信号。通过一系列实际应用，我们证明了所提趋势的计算鲁棒性和实用价值，强调了它们在多样化时间序列环境中的适应性和相关性。
英文摘要：
In this paper we revisit the problem of decomposing a signal into a tendency and a residual. The tendency describes an executive summary of a signal that encapsulates its notable characteristics while disregarding seemingly random, less interesting aspects. Building upon the Intrinsic Time Decomposition (ITD) and information-theoretical analysis, we introduce two alternative procedures for selecting the tendency from the ITD baselines. The first is based on the maximum extrema prominence, namely the maximum difference between extrema within each baseline. Specifically this method selects the tendency as the baseline from which an ITD step would produce the largest decline of the maximum prominence. The second method uses the rotations from the ITD and selects the tendency as the last baseline for which the associated rotation is statistically stationary. We delve into a comparative analysis of the information content and interpretability of the tendencies obtained by our proposed methods and those obtained through conventional low-pass filtering schemes, particularly the Hodrik-Prescott (HP) filter. Our findings underscore a fundamental distinction in the nature and interpretability of these tendencies, highlighting their context-dependent utility with emphasis in multi-scale signals. Through a series of real-world applications, we demonstrate the computational robustness and practical utility of our proposed tendencies, emphasizing their adaptability and relevance in diverse time series contexts.
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。
