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Asymptotic Properties of GARCH-X Processes

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  • Heejoon Han

Abstract

This article considers a GARCH process, generally named as GARCH-X, in which the additional covariate is specified as a positive fractionally integrated process. Recent work on MEM, HEAVY, and Realized GARCH models falls in this category. We investigate the asymptotic properties of this process and show how it explains stylized facts of financial time series such as the long memory property in volatility and leptokurtosis. Not surprisingly, the time series properties of the GARCH-X process with a nonstationary covariate are qualitatively different from those of the GARCH-X process with a stationary covariate. Nevertheless, if the covariate is persistent, the GARCH-X process provides adequate explanations of some stylized facts that the GARCH(1,1) model cannot capture.

Suggested Citation

  • Heejoon Han, 2015. "Asymptotic Properties of GARCH-X Processes," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 188-221.
    • Handle: RePEc:oup:jfinec:v:13:y:2015:i:1:p:188-221.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbt023
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    Citations

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    Cited by:

    1. Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2019. "Testing Garch-X Type Models," Econometric Theory, Cambridge University Press, vol. 35(5), pages 1012-1047, October.
    2. Heejoon Han & Myung D. Park & Shen Zhang, 2015. "A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 209-219, April.
    3. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    4. Huang, Junbo & Tian, Huiting & Shen, Weibing, 2023. "Characteristics and mechanisms of the U.S. stock market spillover effects on the Chinese A-share market: Evidence from 6 A-share broad-based and 31 sector indices," International Review of Financial Analysis, Elsevier, vol. 87(C).
    5. Conrad, Christian & Kleen, Onno, 2016. "On the statistical properties of multiplicative GARCH models," Working Papers 0613, University of Heidelberg, Department of Economics.
    6. Holger Fink & Andreas Fuest & Henry Port, 2018. "The Impact of Sovereign Yield Curve Differentials on Value-at-Risk Forecasts for Foreign Exchange Rates," Risks, MDPI, vol. 6(3), pages 1-19, August.
    7. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    8. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2023. "Exploring volatility of crude oil intraday return curves: A functional GARCH-X model," Journal of Commodity Markets, Elsevier, vol. 32(C).
    9. Naimoli, Antonio, 2022. "The information content of sentiment indices for forecasting Value at Risk and Expected Shortfall in equity markets," MPRA Paper 112588, University Library of Munich, Germany.
    10. M. Karanasos & S. Yfanti & J. Hunter, 2022. "Emerging stock market volatility and economic fundamentals: the importance of US uncertainty spillovers, financial and health crises," Annals of Operations Research, Springer, vol. 313(2), pages 1077-1116, June.
    11. Julien Chevallier & Bilel Sanhaji, 2023. "Jump-Robust Realized-GARCH-MIDAS-X Estimators for Bitcoin and Ethereum Volatility Indices," Stats, MDPI, vol. 6(4), pages 1-32, December.
    12. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2021. "Exploring volatility of crude oil intra-day return curves: a functional GARCH-X Model," MPRA Paper 109231, University Library of Munich, Germany.
    13. M. Karanasos & S. Yfanti & A. Christopoulos, 2021. "The long memory HEAVY process: modeling and forecasting financial volatility," Annals of Operations Research, Springer, vol. 306(1), pages 111-130, November.
    14. Naimoli, Antonio, 2023. "The information content of sentiment indices in forecasting Value at Risk and Expected Shortfall: a Complete Realized Exponential GARCH-X approach," International Economics, Elsevier, vol. 176(C).
    15. Zhang, Chuanhai & Ma, Huan & Arkorful, Gideon Bruce & Peng, Zhe, 2023. "The impacts of futures trading on volatility and volatility asymmetry of Bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 86(C).
    16. Huang, Zhuo & Liu, Hao & Wang, Tianyi, 2016. "Modeling long memory volatility using realized measures of volatility: A realized HAR GARCH model," Economic Modelling, Elsevier, vol. 52(PB), pages 812-821.
    17. Conrad, Christian & Schienle, Melanie, 2015. "Misspecification Testing in GARCH-MIDAS Models," Working Papers 0597, University of Heidelberg, Department of Economics.
    18. Guglielmo Maria Caporale & Menelaos Karanasos & Stavroula Yfanti, 2019. "Macro-Financial Linkages in the High-Frequency Domain: The Effects of Uncertainty on Realized Volatility," CESifo Working Paper Series 8000, CESifo.

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