We develop an adaptive jump test for discretely observed high-frequency semimartingales by combining the A"it-Sahalia--Jacod ratio statistic (A"it-Sahalia and Jacod, 2009) and the Lee--Mykland extreme-return statistic (Lee and Mykland, 2008) with the Cauchy combination rule. Allowing stochastic It^o drift, volatility, and leverage, we show asymptotic independence under the continuous-path null and dense local alternatives, yielding an analytically calibrated test with closed-form power; under finite-activity jumps, the test is consistent. We also extend the method to additive microstructure noise. Simulations show that the combined procedure performs well under both dense and sparse alternatives and is typically best overall.

翻译：我们通过结合Aït-Sahalia与Jacod的比率统计量（Aït-Sahalia和Jacod, 2009）以及Lee与Mykland的极端收益统计量（Lee和Mykland, 2008）与Cauchy组合法则，开发了一种针对离散观测高频半鞅的自适应跳跃检验。在允许随机Itô漂移、波动率和杠杆效应的条件下，我们证明了在连续路径原假设和密集局部备择假设下的渐近独立性，从而得到一个具有解析形式功效的解析校准检验；在有限活动跳跃情形下，该检验是一致的。我们还将该方法推广至加性微观结构噪声情形。模拟结果表明，该组合过程在密集和稀疏备择假设下均表现良好，且通常为全局最优。