Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance
Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance
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DOI：
10.2139/ssrn.2475620
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
P. Mykland;Lan Zhang
中科院分区：
文献类型：
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作者：
P. Mykland;Lan Zhang
高频金融数据的可用性产生了一系列基于日内数据的估计器，提高了大范围金融计量经济学的质量。然而，估计这些估计量的标准误差往往是具有挑战性的。问题的根源在于，传统上，标准误差依赖于估计理论推导的渐近方差，并且该渐近方差通常涉及比待估计的原始参数复杂得多的量。标准误差很重要：它们被用来以置信区间的形式评估估计量的精确度，创建用于测试的“可行统计量，根据例如每日估计建立预测模型，以及优化调整参数。本文的贡献是提供一个替代和一般的解决方案，这个问题，我们称之为观测渐近方差。它是一种用于评估渐近方差（AVAR）的通用非参数方法。它为一大类综合参数Θ = θ t dt提供了AVAR的一致估计，其中点参数过程θ可以是一般的半鞅，具有连续和跳跃分量。所观察到的AVAR在双尺度方法的帮助下实现。它的结构在存在微结构噪声的情况下工作良好，并且在多变量情况下，当观察时间是不规则的或异步的。该方法适用于各种各样的估计量，包括方差和协方差的标准估计量，也适用于更复杂的估计量，如杠杆效应、高频贝塔和半方差。
The availability of high frequency financial data has generated a series of estimators based on intra‐day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θ t dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.