This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular observations, sampled at different frequencies. We develop central limit theorems for the statistics under the respective null hypotheses and apply bootstrap procedures to assess the limiting distributions. Further we define corrected statistics to improve the finite sample performance. Simulations show that the test based on our corrected statistic yields good results and even outperforms existing tests in the case of regular observations.

中文翻译：

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在不规则和异步观察的情况下（常见）跳跃的零假设

本文提出了针对单变量半鞅中不存在跳跃和双变量半鞅中不存在常见跳跃的新测试。我们的方法依赖于基于不规则观察的功率变化比率统计，以不同频率采样。我们在各自的零假设下为统计量制定了中心极限定理，并应用引导程序来评估极限分布。此外，我们定义了更正的统计数据以提高有限样本性能。模拟表明，基于我们校正的统计量的测试产生了良好的结果，甚至在常规观察的情况下优于现有的测试。