Applications of distance correlation to time series
Applications of distance correlation to time series
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DOI：
10.3150/17-bej955
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发表时间：
2018-11-01
期刊：
影响因子：
1.5
通讯作者：
Wan, Phyllis
中科院分区：
文献类型：
--
作者：
Davis, Richard A.;Matsui, Muneya;Wan, Phyllis
使用经验特征函数进行推断问题，包括一些特殊参数设置下的估计和拟合优度检验，有着悠久的历史，可以追溯到70年代。最近，在其他推理设置中使用经验特征函数的兴趣重新燃起。Szekely等人开发的距离协方差和相关性（Ann. Statist. 35（2007）2769-2794）以及Szekely和Rizzo（Ann. Appl. Stat. 3（2009）1236-1265），用于测量两个随机向量之间的依赖性和测试独立性，也许是对此最著名的说明。我们将这些想法应用于平稳的单变量和多变量时间序列来测量时间序列中的滞后自相关和交叉相关。在强混合假设下，我们建立了样本自相关函数和互距离相关函数的渐近理论。我们还将自距离相关函数（ADCF）应用于自回归过程的残差，作为拟合优度的测试。在自回归模型为真的情况下，经验ADCF的极限分布可能与基于i.i.d.的相应极限分布显著不同。顺序我们说明了使用经验的自相关函数和交叉距离相关函数在各种情况下测试时间序列的依赖性和交叉依赖性。
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s. More recently, there has been renewed interest in using empirical characteristic functions in other inference settings. The distance covariance and correlation, developed by Szekely et al. (Ann. Statist. 35 (2007) 2769-2794) and Szekely and Rizzo (Ann. Appl. Stat. 3 (2009) 1236-1265) for measuring dependence and testing independence between two random vectors, are perhaps the best known illustrations of this. We apply these ideas to stationary univariate and multivariate time series to measure lagged auto- and cross-dependence in a time series. Assuming strong mixing, we establish the relevant asymptotic theory for the sample auto-and cross-distance correlation functions. We also apply the auto-distance correlation function (ADCF) to the residuals of an autoregressive processes as a test of goodness of fit. Under the null that an autoregressive model is true, the limit distribution of the empirical ADCF can differ markedly from the corresponding one based on an i.i.d. sequence. We illustrate the use of the empirical auto-and cross-distance correlation functions for testing dependence and cross-dependence of time series in a variety of contexts.