We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the adaptive estimator and provide three types of test statistics: likelihood ratio type test, Wald type test and Rao’s score type test. It is proved that these test statistics converge in distribution to the chi-squared distribution under null hypothesis and have consistency of the tests against alternatives. Moreover, these test statistics converge in distribution to the non-central chi-squared distribution under local alternatives. We also give some simulation studies of the behavior of the three types of test statistics.

我们考虑基于高频数据的多维遍历扩散的参数测试。我们提出了扩散参数和漂移参数的两步测试方法。为了构建测试的测试统计量，我们利用自适应估计器并提供三种类型的测试统计量：似然比类型测试、Wald 类型测试和 Rao 分数类型测试。事实证明，这些检验统计量在零假设下的分布收敛于卡方分布，并且具有针对备选方案的检验的一致性。此外，这些测试统计量在分布上收敛于局部备选方案下的非中心卡方分布。我们还对三种类型的测试统计的行为进行了一些模拟研究。