Multifrequency-Band Tests for White Noise Under Heteroscedasticity
提出一类基于最大重叠离散小波包变换的多频带检验方法，用于在异方差数据下检验白噪声假设，并通过数据驱动自动选择尺度，模拟和实例验证了良好性能。
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.