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ARCH/GARCH with persistent covariate: Asymptotic theory of MLE

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  • Han, Heejoon
  • Park, Joon Y.

Abstract

The paper considers a volatility model which introduces a persistent, integrated or near-integrated, covariate to the standard GARCH(1, 1) model. For such a model, we derive the asymptotic theory of the quasi-maximum likelihood estimator. In particular, we establish consistency and obtain limit distribution. The limit distribution is generally non-Gaussian and represented as a functional of Brownian motions. However, it becomes Gaussian if the covariate has innovation uncorrelated with the squared innovation of the model or the volatility function is linear in parameter. We provide a simulation study to demonstrate the relevance and usefulness of our asymptotic theory.

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  • Han, Heejoon & Park, Joon Y., 2012. "ARCH/GARCH with persistent covariate: Asymptotic theory of MLE," Journal of Econometrics, Elsevier, vol. 167(1), pages 95-112.
    • Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:95-112
    DOI: 10.1016/j.jeconom.2011.10.004
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    2. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    3. Niklas Ahlgren & Alexander Back & Timo Terasvirta, 2024. "A new GARCH model with a deterministic time-varying intercept," Papers 2410.03239, arXiv.org, revised Oct 2024.
    4. Theodoros Daglis & Ioannis G. Melissaropoulos & Konstantinos N. Konstantakis & Panayotis G. Michaelides, 2022. "The impact of COVID-19 on global stock markets: early linear and non-linear evidence for Italy," Evolutionary and Institutional Economics Review, Springer, vol. 19(1), pages 485-495, April.
    5. Abdul-Nasir T. Yola, 2019. "On the Reaction of Stock Market to Monetary Policy Innovations: New Evidence from Nigeria," Academic Journal of Economic Studies, Faculty of Finance, Banking and Accountancy Bucharest,"Dimitrie Cantemir" Christian University Bucharest, vol. 5(2), pages 94-98, June.
    6. Ming Chen & Qiongxia Song, 2016. "Semi-parametric estimation and forecasting for exogenous log-GARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 93-112, March.
    7. Kanungo, Rama Prasad, 2021. "Uncertainty of M&As under asymmetric estimation," Journal of Business Research, Elsevier, vol. 122(C), pages 774-793.
    8. Daglis, Theodoros & Konstantakis, Konstantinos N. & Michaelides, Panayotis G. & Papadakis, Theodoulos Eleftherios, 2020. "The forecasting ability of solar and space weather data on NASDAQ’s finance sector price index volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    9. Francq, Christian & Thieu, Le Quyen, 2019. "Qml Inference For Volatility Models With Covariates," Econometric Theory, Cambridge University Press, vol. 35(1), pages 37-72, February.
    10. Romain Menier & Guillaume Bagnarosa & Alexandre Gohin, 2024. "On the dependence structure of European vegetable oil markets," Post-Print hal-04523660, HAL.
    11. Han, Heejoon & Park, Joon Y., 2014. "GARCH with omitted persistent covariate," Economics Letters, Elsevier, vol. 124(2), pages 248-254.

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    More about this item

    Keywords

    ARCH; GARCH; Persistent covariate; Maximum likelihood estimator; Asymptotic distribution theory;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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