On nonparametric and semiparametric testing for multivariate linear time series
On nonparametric and semiparametric testing for multivariate linear time series
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DOI：
10.1214/08-aos610
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发表时间：
2009-09
影响因子：
4.5
通讯作者：
Yoshihiro Yajima;Y. Matsuda
中科院分区：
文献类型：
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作者：
Yoshihiro Yajima;Y. Matsuda
我们以统一的方式制定多元平稳时间序列的非参数和半参数假设检验，并基于谱密度矩阵的估计提出新的检验统计量。这些检验统计量在零假设下的极限分布始终是正态分布，并且在实际应用中很容易实现。然而，如果原假设为假，则随着样本大小 n 趋向无穷大，它们趋向无穷大的速度将快于参数率 n1/2。它们可以应用于各种零假设，例如分量序列之间的独立性、分量序列的自协方差函数或自相关函数的相等性以及协方差矩阵函数的可分离性。
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting distributions of these test statistics under null hypotheses are always normal distributions and they are implemented easily for practical use. While if null hypotheses are false, as n, the sample size, goes to infinity, they diverge to infinity faster than the parametric rate n1/2. They can be applied to various null hypotheses such as the independence between the component series, the equality of the autocovariance functions or the autocorrelation functions of the component series, and the separability of the covariance matrix function.