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Testing for an omitted multiplicative long-term component in GARCH models

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  • Conrad, Christian
  • Schienle, Melanie

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.

Suggested Citation

  • Conrad, Christian & Schienle, Melanie, 2019. "Testing for an omitted multiplicative long-term component in GARCH models," Working Paper Series in Economics 121, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    • Handle: RePEc:zbw:kitwps:121
    DOI: 10.5445/IR/1000090371
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    1. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    2. Opschoor, Anne & van Dijk, Dick & van der Wel, Michel, 2014. "Predicting volatility and correlations with Financial Conditions Indexes," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 435-447.
    3. Cristina Amado & Annastiina Silvennoinen & Timo Teräsvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," CREATES Research Papers 2018-14, Department of Economics and Business Economics, Aarhus University.
    4. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    5. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
    6. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    7. Conrad, Christian & Loch, Karin, 2015. "The variance risk premium and fundamental uncertainty," Economics Letters, Elsevier, vol. 132(C), pages 56-60.
    8. Paye, Bradley S., 2012. "‘Déjà vol’: Predictive regressions for aggregate stock market volatility using macroeconomic variables," Journal of Financial Economics, Elsevier, vol. 106(3), pages 527-546.
    9. 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.
    10. Escanciano, Juan Carlos, 2009. "Quasi-Maximum Likelihood Estimation Of Semi-Strong Garch Models," Econometric Theory, Cambridge University Press, vol. 25(2), pages 561-570, April.
    11. W. K. Li & T. K. Mak, 1994. "On The Squared Residual Autocorrelations In Non‐Linear Time Series With Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 627-636, November.
    12. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    13. Charlotte Christiansen & Maik Schmeling & Andreas Schrimpf, 2012. "A comprehensive look at financial volatility prediction by economic variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 956-977, September.
    14. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    15. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    16. Dorion, Christian, 2016. "Option Valuation with Macro-Finance Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(4), pages 1359-1389, August.
    17. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    18. Scott R. Baker & Nicholas Bloom & Steven J. Davis, 2016. "Measuring Economic Policy Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1593-1636.
    19. Cristina Amado & Timo Teräsvirta, 2017. "Specification and testing of multiplicative time-varying GARCH models with applications," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 421-446, April.
    20. Aruoba, S. BoraÄŸan & Diebold, Francis X. & Scotti, Chiara, 2009. "Real-Time Measurement of Business Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 417-427.
    21. Robert F. Engle & Eric Ghysels & Bumjean Sohn, 2013. "Stock Market Volatility and Macroeconomic Fundamentals," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 776-797, July.
    22. Halunga, Andreea G. & Orme, Chris D., 2009. "First-Order Asymptotic Theory For Parametric Misspecification Tests Of Garch Models," Econometric Theory, Cambridge University Press, vol. 25(2), pages 364-410, April.
    23. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    24. Andreou, Elena, 2016. "On the use of high frequency measures of volatility in MIDAS regressions," CEPR Discussion Papers 11307, C.E.P.R. Discussion Papers.
    25. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    26. Eric Ghysels & Arthur Sinko & Rossen Valkanov, 2007. "MIDAS Regressions: Further Results and New Directions," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 53-90.
    27. Hossein Asgharian & Ai Jun Hou & Farrukh Javed, 2013. "The Importance of the Macroeconomic Variables in Forecasting Stock Return Variance: A GARCH‐MIDAS Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(7), pages 600-612, November.
    28. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    29. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    30. Christian Conrad & Karin Loch, 2015. "Anticipating Long‐Term Stock Market Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(7), pages 1090-1114, November.
    31. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
    32. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(3), pages 563-596, June.
    33. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    34. Li, Muyi & Li, Guodong & Li, Wai Keung, 2011. "Score Tests for Hyperbolic GARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 579-586.
    35. Elena Andreou, 2016. "On the use of high frequency measures of volatility in MIDAS regressions," University of Cyprus Working Papers in Economics 03-2016, University of Cyprus Department of Economics.
    36. Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 8(2), pages 227-236, October.
    37. Muyi Li & Guodong Li & Wai Keung Li, 2011. "Score Tests for Hyperbolic GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 579-586, October.
    38. Wang, Fangfang & Ghysels, Eric, 2015. "Econometric Analysis Of Volatility Component Models," Econometric Theory, Cambridge University Press, vol. 31(2), pages 362-393, April.
    39. Andreou, Elena, 2016. "On the use of high frequency measures of volatility in MIDAS regressions," Journal of Econometrics, Elsevier, vol. 193(2), pages 367-389.
    40. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    2. 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.
    3. 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.
    4. Christian Conrad & Robert F. Engle, 2021. "Modelling Volatility Cycles: The (MF)2 GARCH Model," Working Paper series 21-05, Rimini Centre for Economic Analysis.
    5. Wu, Xinyu & Xie, Haibin, 2021. "A realized EGARCH-MIDAS model with higher moments," Finance Research Letters, Elsevier, vol. 38(C).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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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    More about this item

    Keywords

    GARCH-MIDAS; LM test; Long-Term Volatility; Mixed-Frequency Data; Volatility Component Models;
    All these keywords.

    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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