Mean Tests For High-dimensional Time Series

IF 1.5 3区 数学 Q2 STATISTICS & PROBABILITY Statistica Sinica Pub Date : 2023-01-01 DOI:10.5705/ss.202022.0147
Shuyi Zhang, Songxi Chen, Yumou Qiu
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Abstract

: This paper considers testing for two-sample mean difference with high-dimensional temporally dependent data, which is later extended to the one-sample situation. To eliminate the bias caused by the temporal dependence among the time series observations, a band-excluded U-statistic (BEU) is proposed to estimate the squared Euclidean distance between the two means, which excludes cross-products of data vectors among temporally close time points. The asymptotic normality of the BEU statistic is derived under the high-dimensional setting with “spatial” (column-wise) and temporal dependence. An estimator built on the kernel smoothed cross-time covariances is developed to estimate the variance of the BEU-statistic, which facilitates a test procedure based on the standardized BEU-statistic. The proposed test is nonparametric and adaptive to a wide range of dependence and dimensionality, and has attractive power properties relative to a self-normalized test. Numerical simulation and a real data analysis on the return and volatility of S&P 500 stocks before and after the 2008 financial crisis are conducted to demonstrate the performance and utility of the proposed test.
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高维时间序列的均值检验
本文考虑了高维时变数据的两样本均值差检验,并将其推广到单样本情况。为了消除时间序列观测值之间的时间相关性所造成的偏差,提出了一种排除频带的u统计量(BEU)来估计两个均值之间的欧几里得距离的平方,该方法排除了时间上接近的时间点之间数据向量的交叉积。在具有“空间”(列方向)和时间依赖性的高维设置下,导出了BEU统计量的渐近正态性。提出了一种基于核平滑跨时间协方差的估计器来估计beu统计量的方差,从而简化了基于标准化beu统计量的测试过程。所提出的测试是非参数的,可适应大范围的依赖和维度,并且相对于自归一化测试具有吸引力的功率特性。通过对2008年金融危机前后标准普尔500指数股票收益率和波动性的数值模拟和实际数据分析,证明了所提出的检验方法的有效性和实用性。
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来源期刊
Statistica Sinica
Statistica Sinica 数学-统计学与概率论
CiteScore
2.10
自引率
0.00%
发文量
82
审稿时长
10.5 months
期刊介绍: Statistica Sinica aims to meet the needs of statisticians in a rapidly changing world. It provides a forum for the publication of innovative work of high quality in all areas of statistics, including theory, methodology and applications. The journal encourages the development and principled use of statistical methodology that is relevant for society, science and technology.
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