This paper addresses the long-standing challenge of estimating the leverage effect from high-frequency data contaminated by dependent, non-Gaussian microstructure noise. We depart from the conventional reliance on pre-averaging or volatility "plug-in" methods by introducing a holistic multi-scale framework that operates directly on the leverage effect. We propose two novel estimators: the Subsampling-and-Averaging Leverage Effect (SALE) and the Multi-Scale Leverage Effect (MSLE). Central to our approach is a shifted window technique that constructs a noise-unbiased base estimator, significantly simplifying the multi-scale architecture. We provide a rigorous theoretical foundation for these estimators, establishing central limit theorems and stable convergence results that remain valid under both noise-free and dependent-noise settings. The primary contribution to estimation efficiency is a specifically designed weighting strategy for the MSLE estimator. By optimizing the weights based on the asymptotic covariance structure across scales and incorporating finite-sample variance corrections, we achieve substantial efficiency gains over existing benchmarks. Extensive simulation studies and an empirical analysis of 30 U.S. assets demonstrate that our framework consistently yields smaller estimation errors and superior performance in realistic, noisy market environments.
翻译:本文解决了从受依赖、非高斯微观结构噪声污染的高频数据中估计杠杆效应这一长期存在的难题。我们摒弃了传统上对预平均或波动率"插件"方法的依赖,引入了一种直接针对杠杆效应进行操作的**整体多尺度框架**。我们提出了两种新颖的估计量:**子采样平均杠杆效应**和**多尺度杠杆效应**。我们方法的核心是一种**平移窗口技术**,它构建了一个噪声无偏的基估计量,从而显著简化了多尺度架构。我们为这些估计量提供了严格的理论基础,建立了中心极限定理和稳定收敛结果,这些结果在无噪声和依赖噪声两种设定下均成立。对估计效率的主要贡献在于为MSLE估计量专门设计的**加权策略**。通过基于跨尺度的渐近协方差结构优化权重,并纳入有限样本方差校正,我们相对于现有基准方法实现了显著的效率提升。大量的模拟研究以及对30种美国资产的实证分析表明,在现实、充满噪声的市场环境中,我们的框架始终能产生更小的估计误差和更优越的性能。