Conditional quantile analysis for realized GARCH models

Abstract

This article introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized generalized autoregressive conditional heteroskedasticity (GARCH) model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two-step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi-maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite-sample performance. Finally, we apply the proposed methodology to calculate the value at risk of 20 individual assets and compare its performance with existing competitors.