Testing for Vector White Noise Using Maximum Cross Correlations

• Activity Number: 294
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Jinyuan Chang* and Qiwei Yao and Wen Zhou
• Companies: University of Melbourne and London School of Economics and Colorado State University
• Keywords: Cross correlations ; Normal approximation ; Parametric bootstrap ; PCA for time series ; Portmanteau test ; Vector white noise

Abstract

We propose a new omnibus test for vector white noise using the maximum absolute auto-/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 the three multivariate versions of the Box-Pierce portmanteau test especially when the dimension of time series is high. 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 (2015).