An Efficient Multi-scale Leverage Effect Estimator under Dependent Microstructure Noise

ArXiv ID: 2505.08654 “View on arXiv”

Authors: Ziyang Xiong, Zhao Chen, Christina Dan Wang

Abstract

Estimating the leverage effect from high-frequency data is vital but challenged by complex, dependent microstructure noise, often exhibiting non-Gaussian higher-order moments. This paper introduces a novel multi-scale framework for efficient and robust leverage effect estimation under such flexible noise structures. We develop two new estimators, the Subsampling-and-Averaging Leverage Effect (SALE) and the Multi-Scale Leverage Effect (MSLE), which adapt subsampling and multi-scale approaches holistically using a unique shifted window technique. This design simplifies the multi-scale estimation procedure and enhances noise robustness without requiring the pre-averaging approach. We establish central limit theorems and stable convergence, with MSLE achieving convergence rates of an optimal $n^{"-1/4"}$ and a near-optimal $n^{"-1/9"}$ for the noise-free and noisy settings, respectively. A cornerstone of our framework’s efficiency is a specifically designed MSLE weighting strategy that leverages covariance structures across scales. This significantly reduces asymptotic variance and, critically, yields substantially smaller finite-sample errors than existing methods under both noise-free and realistic noisy settings. Extensive simulations and empirical analyses confirm the superior efficiency, robustness, and practical advantages of our approach.

Keywords: Multi-scale Framework, Subsampling-and-Averaging Leverage Effect (SALE), Non-Gaussian Microstructure Noise, Convergence Rates, High-frequency Data, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, featuring advanced theoretical derivations, central limit theorems, and convergence rate analyses, warranting a high math score. It also demonstrates high empirical rigor through extensive Monte Carlo simulations, validation of theoretical properties, and real-world high-frequency data analysis on multiple assets.

  flowchart TD
    A["Research Goal: Efficient Leverage Effect Estimation<br>under Dependent Microstructure Noise"] --> B["Methodology: Multi-scale Framework<br>with Shifted Windows & Holistic Subsampling"]
    
    subgraph C ["Data & Inputs"]
        direction LR
        C1["High-Frequency Equity Data"]
        C2["Dependent &<br>Non-Gaussian Noise"]
    end
    
    B --> C
    C --> D["Computational Process:<br>MSLE & SALE Estimators<br>Optimal Weighting Strategy"]
    
    D --> E["Outcomes"]
    
    subgraph E ["Key Findings"]
        direction TB
        E1["Convergence Rates:<br>Optimal n^{"-1/4"} (noise-free)<br>Near-optimal n^{"-1/9"} (noisy)"]
        E2["Superior Efficiency & Robustness:<br>Lower asymptotic variance &<br>smaller finite-sample errors vs. existing methods"]
        E3["Simplified Multi-scale Estimation:<br>No pre-averaging needed"]
    end