We establish a feasible central limit theorem with convergence rate $n^{1/8}$ for the estimation of the integrated volatility of volatility (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show that a more powerful test can be established based on a VoV estimator with a convergence rate $n^{1/5}$ under the null. Empirical results on the S&P 500 and individual stocks show strong evidence of non-zero VoV.

我们建立了一个具有收敛速度的可行中心极限定理$n^{1/8}$用于基于带有跳跃的嘈杂高频数据估计波动率的综合波动率（VoV）。这是在这种通用设置下为 VoV 估计建立的第一个推理理论。中心极限定理用于提供 VoV 的区间估计并进行假设检验。此外，当人们对 VoV 为零的零假设感兴趣时，我们表明可以基于具有收敛速度的 VoV 估计器建立更强大的测试$n^{1/5}$在空值下。标准普尔 500 指数和个股的实证结果显示了非零 VoV 的有力证据。