High Frequency ANOVA that is Robust to Jumps, Microstructure Noise and Asynchronous Observation Times

This article develops the necessary methodology for high frequency ANOVA, focusing on the estimations of idiosyncratic volatility and averaged R-Squared. As a nonlinear and complicated functional of the spot covariance matrix, idiosyncratic volatility estimation poses significant challenges, particularly with jumps, microstructure noise, and asynchronous observation times. Averaged R-Squared, a newly introduced quantity in high frequency econometrics, provides a measure of goodness-of-fit and allows for time-varying features for the coefficient of determination. This article extends the existing theories of Truncated S-TSRV and integrated volatility functional estimation to the case with price/volatility jumps, microstructure noise, and asynchronous/irregular observation times simultaneously. As an additional theoretical contribution, this article proposes the central limit theorems for the functional of integrated volatility functionals (FIVF). Monte Carlo simulations confirm the robustness of our estimators. Empirical studies are conducted to investigate the empirical features of the idiosyncratic volatility estimate, and the averaged R-Squared estimate.