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Unified discrete-time and continuous-time models and statistical inferences for merged low-frequency and high-frequency financial data

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  • Kim, Donggyu
  • Wang, Yazhen

Abstract

This paper introduces a unified model, which can accommodate both continuous-time Itô processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. This model is called a unified GARCH-Itô model. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the low-frequency GARCH structure to develop parameter estimation methods for the combined high-frequency and low-frequency data. We establish asymptotic theory for the proposed estimators and conduct a simulation study to check finite sample performances of the estimators. We apply the proposed estimation approach to Bank of America stock price data.

Suggested Citation

  • Kim, Donggyu & Wang, Yazhen, 2016. "Unified discrete-time and continuous-time models and statistical inferences for merged low-frequency and high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 220-230.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:2:p:220-230
    DOI: 10.1016/j.jeconom.2016.05.003
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    Cited by:

    1. Song, Xinyu & Kim, Donggyu & Yuan, Huiling & Cui, Xiangyu & Lu, Zhiping & Zhou, Yong & Wang, Yazhen, 2021. "Volatility analysis with realized GARCH-Itô models," Journal of Econometrics, Elsevier, vol. 222(1), pages 393-410.
    2. Kim, Donggyu & Song, Xinyu & Wang, Yazhen, 2022. "Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Minseog Oh & Donggyu Kim, 2024. "Effect of the U.S.–China Trade War on Stock Markets: A Financial Contagion Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 22(4), pages 954-1005.
    4. Huiling Yuan & Yulei Sun & Lu Xu & Yong Zhou & Xiangyu Cui, 2022. "A new volatility model: GQARCH‐ItÔ model," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 345-370, May.
    5. Jianqing Fan & Donggyu Kim & Minseok Shin & Yazhen Wang, 2024. "Factor and Idiosyncratic VAR-Ito Volatility Models for Heavy-Tailed High-Frequency Financial Data," Working Papers 202415, University of California at Riverside, Department of Economics.
    6. Huiling Yuan & Yong Zhou & Zhiyuan Zhang & Xiangyu Cui, 2019. "Forecasting security's volatility using low-frequency historical data, high-frequency historical data and option-implied volatility," Papers 1907.02666, arXiv.org.
    7. Chun, Dohyun & Cho, Hoon & Ryu, Doojin, 2023. "Discovering the drivers of stock market volatility in a data-rich world," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 82(C).
    8. Huiling Yuan & Guodong Li & Junhui Wang, 2022. "High-Frequency-Based Volatility Model with Network Structure," Papers 2204.12933, arXiv.org.
    9. 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.
    10. Kim, Donggyu & Fan, Jianqing, 2019. "Factor GARCH-Itô models for high-frequency data with application to large volatility matrix prediction," Journal of Econometrics, Elsevier, vol. 208(2), pages 395-417.
    11. Jin Yu Fu & Jin Guan Lin & Guangying Liu & Hong Xia Hao, 2024. "Statistical inference for GQARCH‐Itô‐jumps model based on the realized range volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(4), pages 613-638, July.
    12. Donggyu Kim & Minseok Shin, 2023. "Volatility models for stylized facts of high‐frequency financial data," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 262-279, May.
    13. Donggyu Kim & Minseok Shin & Yazhen Wang, 2023. "Overnight GARCH-Itô Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1215-1227, October.
    14. Fu, Jin-Yu & Lin, Jin-Guan & Hao, Hong-Xia, 2023. "Volatility analysis for the GARCH–Itô–Jumps model based on high-frequency and low-frequency financial data," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1698-1712.
    15. Yuan, Huiling & Zhou, Yong & Xu, Lu & Sun, Yulei & Cui, Xiangyu, 2020. "A New Volatility Model: GQARCH-Ito Model," SocArXiv hkzdr, Center for Open Science.
    16. Donggyu Kim & Minseok Shin, 2024. "Robust High-Dimensional Time-Varying Coefficient Estimation," Working Papers 202417, University of California at Riverside, Department of Economics.
    17. Donggyu Kim, 2021. "Exponential GARCH-Ito Volatility Models," Papers 2111.04267, arXiv.org.

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    More about this item

    Keywords

    GARCH; Itô process; Quasi-maximum likelihood estimator; Realized volatility; Stochastic differential equation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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