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.

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基于高频金融数据的金融波动状态异质性分析

最近，为了说明低频市场动态，已经开发了几种采用高频金融数据的波动率模型。然而，在金融市场中，我们经常观察到金融波动过程取决于经济状态，因此它们具有状态异质结构。在本文中，为了研究基于高频数据的状态异质市场动态，我们引入了一种基于连续 Itô 扩散过程的新型波动率模型，该模型的日内瞬时波动率过程取决于外生状态变量及其综合波动率。我们称之为状态异构 GARCH-Itô (SG-Itô) 模型。我们建议使用已实现的波动率代理的准似然估计程序并建立其渐近行为。此外，为了测试低频状态异质性，我们开发了 Wald 检验类型的假设检验程序。实证研究结果表明，标准普尔 500 指数波动率存在杠杆、投资者注意力、市场流动性不足、股市联动和节后效应。