In this paper, we decompose the volatility of a diffusion process into systematic and idiosyncratic components, which are not identified with observations discretely sampled from univariate process. Using large dimensional high-frequency data and assuming a factor structure, we obtain consistent estimates of the Laplace transforms of the systematic and idiosyncratic volatility processes. Based on the discrepancy between realized bivariate Laplace transform of the pair of systematic and idiosyncratic volatility processes and the product of the two marginal Laplace transforms, we propose a Kolmogorov–Smirnov-type independence test statistics for the two components of the volatility process. A functional central limit theorem for the discrepancy is established under the null hypothesis that the systematic and idiosyncratic volatilities are independent. The limiting Gaussian process is realized by a simulated discrete skeleton process which can be applied to define an approximate critical region for an independence test.

中文翻译：

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大维高频数据系统性和异质性波动率的渐近

在本文中，我们将扩散过程的波动性分解为系统的和异质的成分，这些成分没有通过从单变量过程中离散采样的观察结果来识别。使用大维高频数据并假设因子结构，我们获得了系统和异质波动过程的拉普拉斯变换的一致估计。基于实现的系统和异质波动过程对的二元拉普拉斯变换与两个边际拉普拉斯变换的乘积之间的差异，我们提出了波动过程的两个分量的 Kolmogorov-Smirnov 型独立检验统计量。在系统波动率和异质波动率相互独立的零假设下，建立了差异的功能中心极限定理。限制高斯过程是通过模拟离散骨架过程实现的，该过程可用于定义独立性测试的近似临界区域。