A LOCAL GAUSSIAN BOOTSTRAP METHOD FOR REALIZED VOLATILITY AND REALIZED BETA
已实现波动率与已实现贝塔的局部高斯自助法AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究高频收益构造的已实现波动率、贝塔及其自助推断。
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已实现波动率与已实现贝塔的局部高斯自助法
- 研究问题
- 如何利用高频收益构造自助样本，估计已实现波动率与贝塔的渐近分布，并改善相关置信区间的近似精度？
- 方法与思路
- 作者将连续收益划为不重叠区块，依据各块已实现方差生成零均值高斯观测，并分析自助分布的累积量匹配。
- 材料陈述的贡献
- 摘要称该方法具有一阶一致性，对已实现波动率提供三阶精化，对已实现贝塔提供二阶精化，并给出模拟与实证比较。
- 阅读关注点
- 核对区块长度与采样频率的关系、连续半鞅条件及学生化方式，尤其关注四阶累积量匹配如何支持高阶精化。
- 阅读边界
- 仅据所给 Crossref 摘要，不能判断具体区块选择及有限样本改进幅度；摘要中的连续价格过程条件也限制了直接推广。
原文摘要
This article introduces a local Gaussian bootstrap method useful for the estimation of the asymptotic distribution of high-frequency data-based statistics such as functions of realized multivariate volatility measures as well as their asymptotic variances. The new approach consists of dividing the original data into nonoverlapping blocks of M consecutive returns sampled at frequency h (where h −1 denotes the sample size) and then generating the bootstrap observations at each frequency within a block by drawing them randomly from a mean zero Gaussian distribution with a variance given by the realized variance computed over the corresponding block. Our main contributions are as follows. First, we show that the local Gaussian bootstrap is first-order consistent when used to estimate the distributions of realized volatility and realized betas under assumptions on the log-price process which follows a continuous Brownian semimartingale process. Second, we show that the local Gaussian bootstrap matches accurately the first four cumulants of realized volatility up to o ( h ), implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009, Econometrica 77(1), 283–306), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able to provide second-order refinements for the realized beta, which is also an improvement of the existing bootstrap results in Dovonon, Gonçalves, and Meddahi (2013, Journal of Econometrics 172, 49–65) (where the pairs bootstrap was shown not to be second-order correct under general stochastic volatility). In addition, we highlight the connection between the local Gaussian bootstrap and the local Gaussianity approximation of continuous semimartingales established by Mykland and Zhang (2009, Econometrica 77, 1403–1455) and show the suitability of this bootstrap method to deal with the new class of estimators introduced in that article. Lastly, we provide Monte Carlo simulations and use empirical data to compare the finite sample accuracy of our new bootstrap confidence intervals for integrated volatility with the existing results.