The Realized Empirical Distribution Function of Stochastic Variance with Application to Goodness-of-Fit Testing

2018-07-03

Journal of Econometrics

AI Summary

This study addresses the challenge of estimating the full-support distribution of the latent instantaneous variance of asset log-prices from noisy high-frequency financial data. It proposes a nonparametric realized empirical distribution function (REDF) that consistently estimates this distribution and, based on it, develops a novel goodness-of-fit test for stochastic volatility models, exhibiting both correct size and high power. The theoretical justification relies on a double-asymptotic framework, and Monte Carlo simulations confirm the method’s finite-sample validity. Empirical analysis reveals that while the inverse Gaussian distribution provides a reasonable fit for equity volatility, more flexible three-parameter alternatives such as the generalized inverse Gaussian may offer superior adaptability. This work represents the first nonparametric, consistent estimation of the volatility distribution from noisy high-frequency data and introduces a new diagnostic tool for stochastic volatility model evaluation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Problem

• stochastic volatility
• empirical distribution function
• goodness-of-fit testing
• high-frequency data
• realized variance

Innovation

• Realized EDF
• stochastic volatility
• goodness-of-fit testing
• nonparametric estimation
• high-frequency data