Conditional quantile estimation for GARCH model based on mixed-frequency data

Zhenming Zhang, Shishun Zhao, Jianhua Cheng () and Jiamin Li
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Zhenming Zhang: Jilin University
Shishun Zhao: Jilin University
Jianhua Cheng: Jilin University
Jiamin Li: Jilin University

Statistical Papers, 2025, vol. 66, issue 4, No 10, 56 pages

Abstract: Abstract The generalized autoregressive conditional heteroskedasticity (GARCH) model has been taken as one of the most influential ways to describe the heteroscedastic financial time series, and the conditional quantile estimation for the GARCH model is crucial for risk management, asset portfolio as well as many other practical applications. High-frequency data, which refers to financial transaction data collected over short time intervals such as seconds or minutes, have richer information compared to traditional low-frequency data (daily, weekly and monthly data), since they can reflect the microstructure and dynamic changes of the market. Keeping these trends in mind, this paper embeds intraday high-frequency data into the classical low-frequency GARCH model to estimate the conditional quantiles. A new estimator based on these mixed-frequency data is proposed, and a revised test statistic for model checking is also given. We derive the asymptotic properties of our proposed estimators and test statistics, and conduct a series of simulation experiments to evaluate their finite-sample performance. Finally, our model and method are applied to three stock indices, further demonstrating the advantages of the mixed-frequency conditional quantile estimators.

Keywords: High-frequency data; Mixed-frequency conditional quantile estimator; GARCH model; Diagnostic checking; 62F10; 62F03 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01704-y

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