Many studies record replicated time series epochs from different groups with the goal of using frequency domain properties to discriminate between the groups. In many applications, there exists variation in cyclical patterns from time series in the same group. Although a number of frequency domain methods for the discriminant analysis of time series have been explored, there is a dearth of models and methods that account for within-group spectral variability. This article proposes a model for groups of time series in which transfer functions are modeled as stochastic variables that can account for both between-group and within-group differences in spectra that are identified from individual replicates. An ensuing discriminant analysis of stochastic cepstra under this model is developed to obtain parsimonious measures of relative power that optimally separate groups in the presence of within-group spectral variability. The approach possess favorable properties in classifying new observations and can be consistently estimated through a simple discriminant analysis of a finite number of estimated cepstral coefficients. Benefits in accounting for within-group spectral variability are empirically illustrated in a simulation study and through an analysis of gait variability.

中文翻译：

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存在组内光谱变异的时间序列的判别分析

许多研究记录了来自不同组的重复时间序列纪元，目的是使用频域属性来区分组。在许多应用中，同一组中的时间序列的周期性模式存在变化。尽管已经探索了许多用于时间序列判别分析的频域方法，但缺乏解释组内频谱可变性的模型和方法。本文提出了一个时间序列组模型，其中传递函数被建模为随机变量，可以解释从单个重复中识别出的组间和组内的光谱差异。随后在此模型下对随机倒谱进行判别分析，以获得相对功率的简约度量，从而在存在组内光谱可变性的情况下最佳地分离组。该方法在对新观测进行分类方面具有良好的特性，并且可以通过对有限数量的估计倒谱系数进行简单的判别分析来一致地估计。在模拟研究和步态变异性分析中，凭经验说明了考虑组内光谱变异性的好处。