Detection of Changes in Multivariate Time Series With Application to EEG Data
Detection of Changes in Multivariate Time Series With Application to EEG Data
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DOI：
10.1080/01621459.2014.957545
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发表时间：
2015-09-01
影响因子：
3.7
通讯作者：
Ombao, Hernando
中科院分区：
文献类型：
--
作者：
Kirch, Claudia;Muhsal, Birte;Ombao, Hernando
本文的主要贡献是严格开发新的统计方法来检测多元时间序列中的变化点。我们将2007年由Huskova， Praskova和Steinebach提出的得分型变化点统计扩展到向量自回归（VAR）情况和流行病变化选择。我们提出的程序不要求观察到的时间序列实际上遵循VAR模型。相反，遵循从业者隐含使用的策略，我们的方法考虑了模型错误说明，因此我们的检测过程仅使用模型背景进行特征提取。我们导出了检验统计量的渐近分布，并证明了我们的过程的渐近幂为1。所提出的检验统计需要对长期协方差矩阵的逆进行估计，这在高维设置中尤其困难（即，时间序列的维数和参数向量的维数都很大）。因此，我们对所提出的测试统计量进行了鲁棒化，并通过广泛的数值实验研究了它们的有限样本性质。最后，我们将我们的程序应用于脑电图，并证明其在识别认知运动任务中复杂大脑过程的变化点方面的潜在影响。
The primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series. We extend the class of score type change point statistics considered in 2007 by Huskova, Praskova, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative. Our proposed procedures do not require the observed time series to actually follow the VAR model. Instead, following the strategy implicitly employed by practitioners, our approach takes model misspecification into account so that our detection procedure uses the model background merely for feature extraction. We derive the asymptotic distributions of our test statistics and show that our procedure has asymptotic power of 1. The proposed test statistics require the estimation of the inverse of the long-run covariance matrix which is particularly difficult in higher-dimensional settings (i.e., where the dimension of the time series and the dimension of the parameter vector are both large). Thus we robustify the proposed test statistics and investigate their finite sample properties via extensive numerical experiments. Finally, we apply our procedure to electroencephalograms and demonstrate its potential impact in identifying change points in complex brain processes during a cognitive motor task.