We compare two interval time series (ITS) by testing whether their underlying distributions are significantly different or not. To perform hypothesis testing, we make use of the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over a number of frequency bands or scales. We obtain the DWT of the radius and centre of each of the two ITS at different scales, and perform randomisation tests. In order to use a randomisation test, the observations must be uncorrelated; this condition is more or less satisfied since at each scale, the DWT coefficients are approximately uncorrelated with each other. Our proposed test statistic is the ratio of the determinants of the covariance matrix of radius and centre DWTs of the two ITS, at each scale. This test statistic ensures that the variability between the upper and lower bounds of each ITS is encompassed. Simulation studies conducted to evaluate the performance of the test show reasonably good estimates of size and power under most conditions, and applications to real interval time series reveal the practical usefulness of this test.

我们通过测试两个基本时间分布是否基本不同来比较两个时间间隔时间序列（ITS）。为了执行假设检验，我们利用离散小波变换（DWT），该方法将时间序列分解为多个频带或标度上的一组系数。我们获得了不同尺度下两个ITS的半径和中心的DWT，并执行了随机化测试。为了使用随机检验，观察结果必须不相关。该条件或多或少地得到满足，因为在每个尺度上，DWT系数彼此几乎不相关。我们建议的检验统计量是在每个尺度下两个ITS的半径和中心DWT的协方差矩阵的行列式的比率。该测试统计数据可确保涵盖每个ITS上下限之间的差异。为评估测试性能而进行的仿真研究显示，在大多数情况下，尺寸和功率的估计值相当合理，实际间隔时间序列的应用表明该测试的实用性。