Robust Adaptive Rate-Optimal Testing for the White Noise Hypothesis

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.

Article plus Supplementary Material document which groups proofs

References in corpus (2)

• Asymptotic Inference of Autocovariances of Stationary Processes
• Testing for white noise under unknown dependence and its applications to goodness-of-fit for time series models

Cited by in corpus (1)

• A Max-Correlation White Noise Test for Weakly Dependent Time Series