Testing for high-dimensional white noise using maximum cross-correlations

Abstract

We propose a new omnibus test for vector white noise using the maximum absolute auto-correlations and cross-correlations of the component series. Based on the newly established 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 the departure from non-IID white noise. 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, for example, the Lagrange multiplier test and the multivariate Box-Pierce portmanteau tests especially when the dimension of 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 the pre-transformed data obtained via the time series principal component analysis proposed by Chang, Guo and Yao (2014). The proposed procedures have been implemented in an R-package HDtest and is available online at CRAN.

References in corpus (5)

• Regularized estimation in sparse high-dimensional time series models
• Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
• Principal component analysis for second-order stationary vector time series
• Confidence regions for entries of a large precision matrix
• Asymptotic Inference of Autocovariances of Stationary Processes

Cited by in corpus (10)

• Principal component analysis for second-order stationary vector time series
• Modeling High-Dimensional Time Series: A Factor Model with Dynamically Dependent Factors and Diverging Eigenvalues
• Central limit theorems for high dimensional dependent data
• Localizing Changes in High-Dimensional Vector Autoregressive Processes
• Testing the martingale difference hypothesis in high dimension
• Modeling High-Dimensional Unit-Root Time Series
• A Two-Way Transformed Factor Model for Matrix-Variate Time Series
• Spectral Analysis of High-dimensional Time Series
• On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime
• Denoising and Multilinear Projected-Estimation of High-Dimensional Matrix-Variate Factor Time Series