Testing High-dimensional White Noise Based On Modified Portmanteau Tests

For high-dimensional time series, we propose a new test to detect white noise that is not necessarily assumed to be independent and identically distributed.The test can be viewed as a modified portmanteau test in high dimensions, and the critical value of the test statistic is approximated by a multiplier bootstrap method.We provide asymptotic properties of our test under the null hypothesis.The usefulness of our tests is demonstrated by simulations and one real example, particularly for detecting dense alternatives.