In this article, we propose a two-step approach to estimate the volatility function of a jump-diffusion model in noisy data setting. The preaveraging method and threshold technique is used to remove microstructure noise and jumps, respectively. The newly proposed estimator is shown to be consistent and asymptotically normal. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed method.

中文翻译：

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含噪声数据的跳跃扩散模型中波动率函数的非参数估计

在本文中，我们提出了一种两步法来估计噪声数据设置中跳跃扩散模型的波动率函数。预平均法和阈值技术分别用于去除微观结构噪声和跳跃。新提出的估计量被证明是一致且渐近正态的。进行模拟研究和实际数据应用以评估所提出方法的有限样本性能。