Flat-Top Realized Kernel Estimation of Quadratic Covariation With Nonsynchronous and Noisy Asset Prices
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非同步含噪资产价格的平顶已实现核二次协变差估计
- 研究问题
- 面对非同步交易、相关噪声与同步误差，如何估计多资产价格的二次协变差，并确保估计矩阵可用于相关系数和已实现贝塔？
- 方法与思路
- 作者建立同步资产价格的多元加性噪声模型，扩展广义平顶已实现核，并用对称矩阵投影进行有限样本正定修正。
- 材料陈述的贡献
- 摘要称，估计量一致、渐近无偏，以 n^(1/4) 的最优速率具有混合高斯极限；正定修正不改变这些渐近性质。
- 阅读关注点
- 应核对外生与内生噪声条件、同步和采样规则、核估计调参及矩阵投影步骤，并检查模拟和六只股票应用中的比较设定。
- 阅读边界
- 所述性质依赖特定噪声和采样框架，摘要未列全正则条件、调参要求与比较结果；不能据此认定该方法对所有市场数据都更优。
原文摘要
This article develops a general multivariate additive noise model for synchronized asset prices and provides a multivariate extension of the generalized flat-top realized kernel estimators, analyzed earlier by Varneskov (2014), to estimate its quadratic covariation. The additive noise model allows for α-mixing dependent exogenous noise, random sampling, and an endogenous noise component that encompasses synchronization errors, lead-lag relations, and diurnal heteroscedasticity. The various components may exhibit polynomially decaying autocovariances. In this setting, the class of estimators considered is consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. A simple finite sample correction based on projections of symmetric matrices ensures positive definiteness without altering the asymptotic properties of the estimators. It, thereby, guarantees the existence of nonlinear transformations of the estimated covariance matrix such as correlations and realized betas, which inherit the asymptotic properties from the flat-top realized kernel estimators. An empirically motivated simulation study assesses the choice of sampling scheme and projection rule, and it shows that flat-top realized kernels have a desirable combination of robustness and efficiency relative to competing estimators. Last, an empirical analysis of signal detection and out-of-sample predictions for a portfolio of six stocks of varying size and liquidity illustrates the use and properties of the new estimators.