State Heterogeneity Analysis of Financial Volatility using high‐frequency Financial Data

Recently, to account for low‐frequency market dynamics, several volatility models, employing high‐frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this article, to study state heterogeneous market dynamics based on high‐frequency data, we introduce a novel volatility model based on a continuous Itô diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated volatility. We call it the state heterogeneous GARCH‐Itô (SG‐Itô) model. We suggest a quasi‐likelihood estimation procedure with the realized volatility proxy and establish its asymptotic behaviors. Moreover, to test the low‐frequency state heterogeneity, we develop a Wald test‐type hypothesis testing procedure. The results of empirical studies suggest the existence of leverage, investor attention, market illiquidity, stock market comovement, and post‐holiday effect in S&P 500 index volatility.