Asymptotic theory of range-based multipower variation

Overview

This paper develops an asymptotic theory for realized range-based multipower variation applicable to high-frequency asset price data. The framework addresses a fundamental estimation problem: the standard range statistic exhibits bias when price processes incorporate jump components. The research establishes theoretical foundations for constructing hybrid range-based estimators that isolate the diffusive volatility component while maintaining robustness to price jumps.

Methods and approach

The methodology constructs realized range-based multipower variation estimators by extending classical range statistics to multipower settings. The asymptotic theory accommodates sparse high-frequency sampling regimes typical in empirical applications where microstructure noise necessitates subsampling. The framework incorporates jump-robust inference procedures and develops efficiency comparisons against conventional subsampled return-based alternatives. The approach is validated through Monte Carlo simulation and applied to equity transaction data.

Results

The analysis demonstrates that standard range statistics suffer significant bias under jump-contaminated price processes. The proposed hybrid range-based estimators effectively remove this bias and recover the underlying diffusive volatility component. When high-frequency data undergo sparse subsampling to mitigate microstructure noise effects, range-based multipower variations achieve substantial efficiency gains relative to subsampled return estimators. Empirical application to equity transaction data confirms the practical viability of the framework for realized volatility estimation.

Implications

The results establish range-based multipower variation as a theoretically grounded alternative to return-based methods for volatility estimation in jump-contaminated settings. The efficiency gains under sparse sampling are particularly relevant for practitioners managing high-frequency datasets subject to microstructure noise, suggesting potential improvements in volatility estimation and inference procedures used across financial econometrics applications.