论文标题
基于高频数据的厄运扩散过程的自适应测试方法
Adaptive testing method for ergodic diffusion processes based on high frequency data
论文作者
论文摘要
我们考虑了基于高频数据的多维千古扩散的参数测试。我们提出了针对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数据，我们使用自适应估计器并提供三种类型的测试统计信息：似然比类型测试，WALD类型测试和RAO的得分类型测试。事实证明，这些测试统计量会在零假设下分布与卡方分布，并具有针对替代方案的测试一致性。此外，这些测试统计数据将分布分布到本地替代方案下的非中心卡方分布。我们还对三种类型的测试统计数据的行为进行了一些模拟研究。
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.
