{"title":"Mean Tests For High-dimensional Time Series","authors":"Shuyi Zhang, Songxi Chen, Yumou Qiu","doi":"10.5705/ss.202022.0147","DOIUrl":null,"url":null,"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.","PeriodicalId":49478,"journal":{"name":"Statistica Sinica","volume":"1 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistica Sinica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5705/ss.202022.0147","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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.
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.