Multifrequency-Band Tests for White Noise Under Heteroscedasticity

This article proposes a new family of multifrequency-band tests for the white noise hypothesis by using the maximum overlap discrete wavelet packet transform. At each scale, the proposed multifrequency-band test has the chi-square asymptotic null distribution under mild conditions, which allow the data to be heteroscedastic. Moreover, an automatic multifrequency-band test is further proposed by using a data-driven method to select the scale, and its asymptotic null distribution is chi-square with one degree of freedom. Both multifrequency-band and automatic multifrequency-band tests are shown to have the desirable size and power performance by simulation studies, and their usefulness is further illustrated by two applications. As an extension, similar tests are given to check the adequacy of linear time series regression models, based on the unobserved model residuals.

Automated summary

This article introduces a new family of multifrequency-band tests for the white noise hypothesis, which have chi-square asymptotic null distribution and are suitable for heteroscedastic data. An automatic multifrequency-band test is proposed using a data-driven method to select scales. Simulation studies demonstrate the good size and power performance of these tests.