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

Xin Liang; Xingfa Zhang; Yuan Li; Chunliang Deng; Xin Liang; Xingfa Zhang; Yuan Li; Chunliang Deng

doi:10.3934/math.2021206

AIMS Mathematics

2021, Volume 6, Issue 4: 3455-3464. doi: 10.3934/math.2021206

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Research article

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

School of Economics and Statistics, Guangzhou University, Guangzhou, 510006, China

Received: 15 October 2020 Accepted: 13 January 2021 Published: 20 January 2021
MSC : 62G05, 62G20

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.
- volatility function,
- volatility proxy,
- local polynomial estimation
Citation: Xin Liang, Xingfa Zhang, Yuan Li, Chunliang Deng. Daily nonparametric ARCH(1) model estimation using intraday high frequency data[J]. AIMS Mathematics, 2021, 6(4): 3455-3464. doi: 10.3934/math.2021206

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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.

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