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

2025-05-13

AI Summary

Estimating the leverage effect in high-frequency financial data is challenged by strong dependence and non-Gaussian microstructure noise, leading to substantial bias and low efficiency in existing estimators. This paper proposes a robust and efficient multiscale estimation framework, introducing for the first time the dual-estimator architecture of Shifted Adaptive Leverage Estimator (SALE) and Multiscale Leverage Estimator (MSLE). A displaced sliding window scheme simplifies computation, while an adaptive optimal weighting strategy—based on cross-scale covariance—is designed to enhance estimation accuracy. Theoretically, MSLE achieves the convergence rate $n^{-1/9}$ under microstructure noise, the fastest rate established to date for this setting. Finite-sample errors are significantly lower than those of state-of-the-art methods. Monte Carlo simulations and empirical analysis on real market data confirm that the proposed approach delivers superior accuracy, strong robustness against noise and dependence, and practical deployability.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Hardware-aware ML
• Multiagent Systems: Adversarial Agents

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Estimating leverage effect under dependent microstructure noise
• Developing robust multi-scale estimators for noisy data
• Improving convergence rates and reducing asymptotic variance

Innovation

• Multi-scale framework for robust leverage estimation
• Shifted window technique simplifies estimation
• MSLE weighting reduces asymptotic variance