Daily nonparametric ARCH(1) model estimation using intraday high frequency data

Abstract

In this paper, the intraday high-frequency data are used to estimate the volatility function of daily nonparametric ARCH(1) model. A nonparametric volatility proxy model is proposed to achieve this objective. Under regular assumptions, the asymptotic distribution of the proposed estimator is established. The impact of different proxies on the estimation precision is also discussed. Simulation and empirical studies show that using the intraday high frequency data can significantly improve the estimation accuracy of the considered model. The idea of this article can be easily extended to other nonparametric or semiparametric ARCH/GARCH models.

Keywords

• volatility function
• volatility proxy
• local polynomial estimation