The authors propose a two-step test for the two-sample problem of processes of Ornstein-Uhlenbeck type. In the first step, the authors test the equality of correlation structures, based on the least square estimators of the correlation parameters, and the test statistic follows the standard normal distribution. If the null hypothesis is not rejected in the first step, the authors consider a second step to test the equality of marginal distributions, based on the weighted deviation of the empirical characteristic functions; the test statistic has a complicated asymptotic distribution, so that sequential bootstrap method is applied to reach a temporary decision. Simulation studies and real data analysis suggest that the proposed approach performs well in finite samples.

作者针对Ornstein-Uhlenbeck型过程的两样本问题提出了两步检验。第一步，作者根据相关参数的最小二乘估计来测试相关结构的相等性，并且测试统计量遵循标准正态分布。如果第一步不拒绝零假设，那么作者将考虑第二步，根据经验特征函数的加权偏差检验边际分布的相等性。测试统计量具有复杂的渐近分布，因此应用顺序引导法来获得临时决策。仿真研究和实际数据分析表明，该方法在有限样本中表现良好。