Inference from High-Frequency Data: A Subsampling Approach

2016-04-01

AI Summary

This study addresses volatility estimation in high-frequency financial data contaminated by market frictions or microstructure noise. The authors propose an adaptive subsampling approach that directly infers the asymptotic (conditional) covariance matrix of volatility estimators without explicitly modeling the noise structure. By employing time-rescaled statistics over local intervals to assess sampling variability, the method automatically selects tuning parameters while ensuring the resulting covariance matrix is positive semidefinite. Theoretical analysis, Monte Carlo simulations, and empirical applications demonstrate that the proposed estimator is consistent, exhibits strong finite-sample performance, and enables robust and feasible statistical inference.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Intelligent Robots: State Estimation

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
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance–covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

Problem

• high-frequency data
• volatility estimation
• asymptotic covariance matrix
• sampling error
• financial markets

Innovation

• subsampling
• high-frequency data
• asymptotic covariance matrix
• volatility estimation
• microstructure noise