We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

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一般波动率动力学下综合波动率函数的有效估计

我们提供了一种渐近理论来估计一类一般的平滑非线性综合波动泛函。此类泛函可广泛用于使用高频交易数据测量金融风险和估计经济模型。该理论在一般波动动力学下是有效的，它适应了伊藤半鞅（例如，跳跃扩散）和长记忆过程（例如，分数布朗运动）。我们在具有填充渐近线的非标准非遍历设置下建立了半参数效率界限，并表明所提出的估计器达到了这个效率界限。这些关于有效估计的结果进一步扩展到具有不规则采样数据的设置。