This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time points, challenging conventional synchronous methods for parameter estimation and hypothesis testing. To address these challenges, we develop a quasi-likelihood framework that accommodates irregular sampling while integrating adaptive estimation techniques for both drift and diffusion coefficients, thereby enhancing optimization stability and reducing computational burden. We rigorously derive the asymptotic properties of the proposed test statistic, showing that it converges to a chi-squared distribution under the null hypothesis and exhibits consistency under alternatives. Moreover, we establish that the resulting tests are asymptotically uniformly most powerful. Extensive numerical experiments corroborate the theoretical findings and demonstrate that our method outperforms existing nonparametric approaches.

翻译：本文针对非同步采样方案下观测到的扩散过程，提出了一种拟似然比检验方法。高频数据，特别是在金融计量经济学中，常记录于不规则时间点，这对传统的同步参数估计与假设检验方法构成了挑战。为解决这些问题，我们构建了一个拟似然框架，该框架能够适应不规则采样，同时整合了针对漂移系数和扩散系数的自适应估计技术，从而提升了优化稳定性并减轻了计算负担。我们严格推导了所提检验统计量的渐近性质，证明其在原假设下收敛于卡方分布，并在备择假设下具有一致性。此外，我们确立了所得检验是渐近一致最大功效的。大量的数值实验验证了理论结果，并表明我们的方法优于现有的非参数方法。