Frequency Band Analysis of Nonstationary Multivariate Time Series
非平稳多元时间序列的频带分析AI 解读 ↓
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非平稳多元时间序列的频带分析
- 研究问题
- 如何从多元局部平稳时间序列中数据驱动地确定频带边界，使频域摘要尽可能保留信号随时间变化的非平稳动态？
- 方法与思路
- 作者构造基于时变谱密度矩阵差异的 L₂ 距离，推导其渐近性质，并用非参数 bootstrap 检验识别频率分割点及相关谱成分。
- 材料陈述的贡献
- 摘要称，方法提供数据驱动的频带划分与成分检验，并通过模拟和静息态脑电应用展示其刻画时变信号的能力。
- 阅读关注点
- 应核对局部平稳条件、谱估计的平滑选择、频率分割准则、bootstrap 有效性，以及所谓最优频带摘要对应的目标。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收。摘要未给出具体渐近条件及数值结果，应用证据来自脑电数据。
原文摘要
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of interest. However, these methods do not provide data-driven methods for identifying frequency bands that optimally summarize frequency-domain information in the time series. A new method to identify partition points in the frequency space of a multivariate locally stationary time series is proposed. These partition points signify changes across frequencies in the time-varying behavior of the signal and provide frequency band summary measures that best preserve the nonstationary dynamics of the observed series. An $L_2$ norm-based discrepancy measure that finds differences in the time-varying spectral density matrix is constructed, and its asymptotic properties are derived. New nonparametric bootstrap tests are also provided to identify significant frequency partition points and to identify components and cross-components of the spectral matrix exhibiting changes over frequencies. Finite-sample performance of the proposed method is illustrated via simulations. The proposed method is used to develop optimal frequency band summary measures for characterizing time-varying behavior in resting-state electroencephalography (EEG) time series, as well as identifying components and cross-components associated with each frequency partition point.