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Testing for an Omitted Multiplicative Long-Term Component in GARCH Models

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  • Christian Conrad
  • Melanie Schienle

Abstract

We consider the problem of testing for an omitted multiplicative long-term component in GARCH-type models. Under the alternative, there is a two-component model with a short-term GARCH component that fluctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange multiplier statistic for testing the null hypothesis that the variable has no explanatory power. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte Carlo simulation. Our test also covers the mixed-frequency case in which the returns are observed at a higher frequency than the explanatory variable. The usefulness of our procedure is illustrated by empirical applications to S&P 500 return data. Supplementary materials for this article are available online.

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  • Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:2:p:229-242
    DOI: 10.1080/07350015.2018.1482759
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    2. Yun-Shi Dai & Peng-Fei Dai & Wei-Xing Zhou, 2024. "The impact of geopolitical risk on the international agricultural market: Empirical analysis based on the GJR-GARCH-MIDAS model," Papers 2404.01641, arXiv.org.
    3. Afees A. Salisu & Wenting Liao & Rangan Gupta & Oguzhan Cepni, 2023. "Economic Conditions and Predictability of US Stock Returns Volatility: Local Factor versus National Factor in a GARCH-MIDAS Model," Working Papers 202323, University of Pretoria, Department of Economics.
    4. Vincenzo Candila & Giampiero M. Gallo & Lea Petrella, 2020. "Mixed--frequency quantile regressions to forecast Value--at--Risk and Expected Shortfall," Papers 2011.00552, arXiv.org, revised Mar 2023.
    5. Christian Conrad & Robert F. Engle, 2021. "Modelling Volatility Cycles: The (MF)2 GARCH Model," Working Paper series 21-05, Rimini Centre for Economic Analysis.
    6. Wu, Xinyu & Xie, Haibin, 2021. "A realized EGARCH-MIDAS model with higher moments," Finance Research Letters, Elsevier, vol. 38(C).
    7. Conrad, Christian & Glas, Alexander, 2018. "‘Déjà vol’ revisited: Survey forecasts of macroeconomic variables predict volatility in the cross-section of industry portfolios," Working Papers 0655, University of Heidelberg, Department of Economics.
    8. Jian Liu & Ziting Zhang & Lizhao Yan & Fenghua Wen, 2021. "Forecasting the volatility of EUA futures with economic policy uncertainty using the GARCH-MIDAS model," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-19, December.
    9. Amendola, Alessandra & Candila, Vincenzo & Gallo, Giampiero M., 2021. "Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model," Econometrics and Statistics, Elsevier, vol. 20(C), pages 12-28.
    10. Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.
    11. Conrad, Christian & Hartmann, Matthias, 2019. "On the determinants of long-run inflation uncertainty: Evidence from a panel of 17 developed economies," European Journal of Political Economy, Elsevier, vol. 56(C), pages 233-250.

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    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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