We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency asset return data. By showing a feasible CLT for this statistic under the null hypothesis of semimartingale volatility paths, we construct a test with fixed asymptotic size and an asymptotic power equal to one. The test is derived under very general conditions for the data-generating process. In particular, it is robust to jumps with arbitrary activity and to the presence of market microstructure noise. In an application of the test to SPY high-frequency data, we find evidence for rough volatility.

翻译：本文提出了一种非参数检验方法，用于判断资产波动率遵循的是具有有限二次变差路径的标准半鞅过程，还是具有无限二次变差路径的粗糙过程。该检验利用了这样一个事实：当且仅当在高频下波动率增量呈现负自相关时，波动率是粗糙的。其检验统计量基于利用高频资产收益率数据计算的现货波动率估计值增量的样本自协方差。通过在原假设（波动率路径为半鞅）下证明该统计量的一个可行的中心极限定理，我们构建了一个具有固定渐近尺寸且渐近功效为一的检验。该检验是在数据生成过程非常一般的条件下推导得出的。特别地，它对任意活动的跳跃以及市场微观结构噪声的存在具有稳健性。在将该检验应用于SPY高频数据时，我们发现了支持粗糙波动率的证据。