  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 paper, to study state heterogeneous market dynamics based on
high-frequency data, we introduce a novel volatility model based on a
continuous Ito 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-Ito (SG-Ito)
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.
