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Asymptotics for parametric GARCH-in-Mean Models

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  • Conrad, Christian
  • Mammen , Enno

Abstract

In this paper we develop an asymptotic theory for the parametric GARCH-in-Mean model. The asymptotics is based on a study of the volatility as a process of the model parameters. The proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem. Our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model. Nevertheless, our theory does not yet treat all standard specifications of the mean function.

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  • Conrad, Christian & Mammen , Enno, 2015. "Asymptotics for parametric GARCH-in-Mean Models," Working Papers 0579, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0579
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    1. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
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    5. Neil Kellard & Denise Osborn & Jerry Coakley & Christian Conrad & Menelaos Karanasos, 2015. "On the Transmission of Memory in Garch-in-Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 706-720, September.
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    9. repec:awi:wpaper:0473 is not listed on IDEAS
    10. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
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    Cited by:

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    2. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    3. Alessandra Canepa, & Karanasos, Menelaos & Paraskevopoulos, Athanasios & Chini, Emilio Zanetti, 2022. "Forecasting Ination: A GARCH-in-Mean-Level Model with Time Varying Predictability," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202212, University of Turin.
    4. Matthias R. Fengler & Alexander Melnikov, 2018. "GARCH option pricing models with Meixner innovations," Review of Derivatives Research, Springer, vol. 21(3), pages 277-305, October.
    5. Canepa, Alessandra, 2022. "Ination Dynamics and Time-Varying Persistence: The Importance of the Uncertainty Channel," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202211, University of Turin.
    6. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    7. Haytem Troug & Matt Murray, 2020. "Crisis determination and financial contagion: an analysis of the Hong Kong and Tokyo stock markets using an MSBVAR approach," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 48(8), pages 1548-1572, December.
    8. Troug, Haytem Ahmed & Murray, Matt, 2015. "Quantitative Easing in Japan and the UK An Econometric Evaluation of the Impacts of Unconventional Monetary Policy on the Returns of Aggregate Output and Price Levels," MPRA Paper 68707, University Library of Munich, Germany.
    9. Dias, Gustavo Fruet, 2017. "The time-varying GARCH-in-mean model," Economics Letters, Elsevier, vol. 157(C), pages 129-132.
    10. Asai, Manabu, 2023. "Feasible Panel GARCH Models: Variance-Targeting Estimation and Empirical Application," Econometrics and Statistics, Elsevier, vol. 25(C), pages 23-38.
    11. Canepa, Alessandra, 2024. "Inflation dynamics and persistence: The importance of the uncertainty channel," The North American Journal of Economics and Finance, Elsevier, vol. 72(C).
    12. Alessandra Canepa, & Menelaos G. Karanasos & Alexandros G. Paraskevopoulos,, 2019. "Second Order Time Dependent Inflation Persistence in the United States: a GARCH-in-Mean Model with Time Varying Coefficients," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201911, University of Turin.

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    More about this item

    Keywords

    GARCH-in-Mean; stochastic recurrence equations; risk-return relationship;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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