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GARCH Parameter Estimation Using High-Frequency Data

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  • Marcel P. Visser

Abstract

A standard procedure for obtaining parameter values of a GARCH model for financial volatility is the quasi maximum likelihood estimator (QMLE) based on daily close-to-close returns. This paper generalizes the QMLE based on daily returns to a QMLE based on intraday high-frequency data. Volatility proxies, such as the realized volatility or the daily high--low range, are used for estimating the parameters of discrete-time GARCH models. Empirical analysis of the S&P 500 index tick data shows that a well-chosen proxy may reduce the variances of the estimators of the GARCH(1,1) autoregression parameters by a factor 20. C14, C22, C51, G1 Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Suggested Citation

  • Marcel P. Visser, 2011. "GARCH Parameter Estimation Using High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 162-197, Winter.
    • Handle: RePEc:oup:jfinec:v:9:y:2011:i:1:p:162-197
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbq017
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    Cited by:

    1. Georgiana-Denisa Banulescu & Bertrand Candelon & Christophe Hurlin & Sébastien Laurent, 2014. "Do We Need Ultra-High Frequency Data to Forecast Variances?," Working Papers halshs-01078158, HAL.
    2. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    3. Denisa Banulescu-Radu & Christophe Hurlin & Bertrand Candelon & Sébastien Laurent, 2016. "Do We Need High Frequency Data to Forecast Variances?," Annals of Economics and Statistics, GENES, issue 123-124, pages 135-174.
    4. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    5. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    6. Wang, Meng & Chen, Zhao & Wang, Christina Dan, 2018. "Composite quantile regression for GARCH models using high-frequency data," Econometrics and Statistics, Elsevier, vol. 7(C), pages 115-133.
    7. Chen Xilong & Ghysels Eric & Wang Fangfang, 2011. "HYBRID GARCH Models and Intra-Daily Return Periodicity," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-28, February.
    8. Piotr Fiszeder & Grzegorz Perczak, 2013. "A new look at variance estimation based on low, high and closing prices taking into account the drift," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 456-481, November.
    9. Visser, Marcel P., 2008. "Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure," MPRA Paper 11100, University Library of Munich, Germany.
    10. Erdemlioglu, Deniz & Laurent, Sébastien & Neely, Christopher J., 2015. "Which continuous-time model is most appropriate for exchange rates?," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 256-268.
    11. Michael Weylandt & Yu Han & Katherine B. Ensor, 2019. "Multivariate Modeling of Natural Gas Spot Trading Hubs Incorporating Futures Market Realized Volatility," Papers 1907.10152, arXiv.org.
    12. Peter R. Hansen & Asger Lunde & Valeri Voev, 2010. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility," CREATES Research Papers 2010-74, Department of Economics and Business Economics, Aarhus University.
    13. Chih-Wen Hsiao & Ya-Chuan Chan & Mei-Yu Lee & Hsi-Peng Lu, 2021. "Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    14. Zhenming Zhang & Shishun Zhao & Jianhua Cheng & Jiamin Li, 2025. "Conditional quantile estimation for GARCH model based on mixed-frequency data," Statistical Papers, Springer, vol. 66(4), pages 1-56, June.
    15. Chunliang Deng & Xingfa Zhang & Yuan Li & Qiang Xiong, 2020. "Garch Model Test Using High-Frequency Data," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    16. Dohyun Chun & Donggyu Kim, 2022. "State Heterogeneity Analysis of Financial Volatility using high‐frequency Financial Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 105-124, January.
    17. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, "undated". "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, Department of Economics and Business Economics, Aarhus University.
    18. Zhenwei Li & Jing Han & Yuping Song, 2020. "On the forecasting of high‐frequency financial time series based on ARIMA model improved by deep learning," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(7), pages 1081-1097, November.
    19. Alain Hecq & Sébastien Laurent & Franz C. Palm, 2011. "Common Intraday Periodicity," Journal of Financial Econometrics, Oxford University Press, vol. 10(2), pages 325-353, 2012 20 1.

    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G1 - Financial Economics - - General Financial Markets
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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