Robust Adaptive Rate-Optimal Testing for the White Noise Hypothesis

TL;DR

This paper introduces a robust, adaptive testing method for the white noise hypothesis that effectively detects subtle autocorrelations using a data-driven order selection and HAC critical values.

Contribution

It proposes a novel automatic order selection procedure for white noise tests, enhancing detection power for weak autocorrelations with a comprehensive simulation validation.

Findings

Effective detection of autocorrelations smaller than $o(n^{-1/2})$

Good size and power properties demonstrated in simulations

Applicable with Lobato and Kuan-Lee HAC critical values

Abstract

A new test is proposed for the weak white noise null hypothesis. The test is based on a new automatic choice of the order for a Box-Pierce or Hong test statistic. The test uses Lobato (2001) or Kuan and Lee (2006) HAC critical values. The data-driven order choice is tailored to detect a new class of alternatives with autocorrelation coefficients which can be $o(n^{-1/2})$ provided there are enough of them. A simulation experiment illustrates the good behavior of the test both under the weak white noise null and the alternative.