Testing for high-dimensional white noise using maximum cross-correlations
提出一种基于最大绝对值自相关和互相关的新检验方法，用于检验向量白噪声，尤其适用于维度高而样本量小的时间序列，模拟显示优于拉格朗日乘子检验和多元Box-Pierce检验。
SUMMARY We propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the $L_\infty$-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods, including the Lagrange multiplier test and the multivariate Box–Pierce portmanteau tests, especially when the dimension of the time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre-transformed data obtained via the time series principal component analysis proposed by J. Chang, B. Guo and Q. Yao (arXiv:1410.2323). The proposed procedures have been implemented in an R package.