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

TL;DR

This paper introduces a new omnibus test for high-dimensional vector white noise using maximum cross-correlations, which outperforms existing methods especially in high-dimensional settings, and is implemented in an R package.

Contribution

A novel high-dimensional white noise test based on maximum cross-correlations, with validated accuracy, power, and an implementation in R.

Findings

The new test outperforms traditional methods like Lagrange multiplier and Box-Pierce tests.

The test maintains validity for non-IID white noise.

Performance improves with pre-transformed data via PCA.

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.