利用ASCA对时间序列中的循环平稳性进行建模
Modeling cyclostationarity in time series using ASCA
AI总结：
本文提出利用ASCA方法对时间序列中的循环平稳性进行建模，通过分析水温趋势和花粉数据验证其有效性，提升多变量数据的可解释性与推断能力。
摘要：
现代跨学科的数据分析越来越多地依赖时间序列。许多这些数据集表现出循环平稳性，其中模式在规律性地重复，通常跨越多种时间尺度，如每日、每周或年周期。在此背景下，统计推断对于区分真正的底层效应与随机波动至关重要。虽然像方差分析（ANOVA）这样的工具可以提供这种推断，但它们通常缺乏可解释性，并且在处理多变量数据的复杂性时显得力不从心。为了解决这些限制，我们提出了一种使用ANOVA同时成分分析（ASCA）进行循环平稳时间序列探索性分析的统一流程。ASCA是ANOVA的扩展，能够处理单变量和多变量情况。结合PCA的可视化能力，ASCA提供了强大的可解释性选项。ASCA的能力已在实验数据分析中得到充分验证，但其在观测数据如时间序列中的应用仍鲜有探索。我们的工作流程引入了一种利用ASCA对时间依赖数据建模的算法方法，使能够在多个循环平稳时间尺度上进行控制，同时考虑到这种数据类型特有的挑战，如自相关性。此外，我们发现，由于其多变量性质，ASCA在不平衡设计中对因素间变异性分离效果优于ANOVA。我们通过两个现实案例研究展示了该方法的有效性：西班牙 Sierra Nevada 山区山湖的水温趋势，以及西班牙格拉纳达市记录的30年空中花粉趋势。
英文摘要：
Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily, weekly or yearly cycles. In this context, statistical inference is essential to distinguish genuine underlying effects from random variability. While tools like Analysis of Variance (ANOVA) provide such inference, they often lack interpretability and struggle with the complexities of multivariate data. To address these limitations, we propose a unified pipeline for the exploratory analysis of cyclostationary times series using ANOVA Simultaneous Component Analysis (ASCA). ASCA is an extension of ANOVA that is able to work in both univariate and multivariate cases. Combining inference with the visualization capabilities of Principal Component Analysis (PCA), ASCA provides powerful options for interpretability. ASCA's capabilities have been well-established in the analysis of experimental data, but they remain largely unexplored for observational data like time series. Our workflow introduces an algorithmic approach to modeling time-dependent data using ASCA, enabling control over multiple cyclostationary time scales while also accounting for the specific challenges of this type of data, such as autocorrelation. Furthermore, we observed that ASCA provides a better separation of variability across factors than ANOVA in unbalanced designs due to its multivariate nature. We demonstrate the efficacy of this methodology through two real-world case studies: water temperature trends in mountain lakes in Sierra Nevada, Spain, and airborne pollen trends over 30 years recorded in the city of Granada, Spain.
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