Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading
噪声跳跃扩散与非同步交易下积分协方差估计量的自助法AI 解读 ↓
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噪声跳跃扩散与非同步交易下积分协方差估计量的自助法
- 研究问题
- 面对跳跃、相关微观结构噪声和非同步交易，如何估计积分协方差估计量的分布，并构造可靠的方差与区间推断？
- 方法与思路
- 作者将野生双重分块自助法推广到一类积分协变动估计量，并通过适当中心化使其复现回归得分的依赖性与异质性。
- 材料陈述的贡献
- 摘要称建立了多变量情形的一阶渐近有效性，获得半正定自助方差估计，并构造回归系数的百分位及学生化区间。
- 阅读关注点
- 应核对估计量类别、分块与中心化规则、非同步观测和噪声的限制，以及相对高斯近似的模拟改善发生在哪些设计中。
- 阅读边界
- 仅依据所给出版社摘要；理论条件和模拟改善幅度未说明，一阶有效性及有限样本比较不能推及所有噪声、跳跃或交易机制。
原文摘要
We propose a bootstrap method for estimating the distribution (and functionals of it such as the variance) of various integrated covariance matrix estimators. In particular, we first adapt the wild blocks of blocks bootstrap method suggested for the pre-averaged realized volatility estimator to a general class of estimators of integrated covolatility. We then show the first-order asymptotic validity of this method in the multivariate context with a potential presence of jumps, dependent microstructure noise, irregularly spaced and non-synchronous data. Our results justify using the bootstrap to estimate the covariance matrix of a broad class of covolatility estimators. The bootstrap variance estimator is positive semi-definite by construction, an appealing feature that is not always shared by existing variance estimators of the integrated covariance estimator. As an application of our results, we also consider the bootstrap for regression coefficients. We show that the wild blocks of blocks bootstrap, appropriately centered, is able to mimic both the dependence and heterogeneity of the scores. We provide a proof of construction of bootstrap percentile and percentile-t intervals as well as variance estimates in this context. This contrasts the traditional pairs bootstrap which is not able to mimic the score heterogeneity even in the simple case where no microstructure noise is present. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improve the finite sample properties of the alternative approach based on the Gaussian approximation. We illustrate its practical use on high-frequency equity data.