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Garch Parameter Estimation Using High-Frequency Data

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  • Visser, Marcel P.

Abstract

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20.

Suggested Citation

  • Visser, Marcel P., 2008. "Garch Parameter Estimation Using High-Frequency Data," MPRA Paper 9076, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:9076
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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.

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    More about this item

    Keywords

    volatility estimation; quasi maximum likelihood; volatility proxy; Gaussian QMLE; log-Gaussian QMLE; autoregressive conditional heteroscedasticity;
    All these keywords.

    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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