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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.

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. 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.
    3. Linton, Oliver & Perron, Benoit, 2003. "The Shape of the Risk Premium: Evidence from a Semiparametric Generalized Autoregressive Conditional Heteroscedasticity Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 354-367, July.
    4. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
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    Cited by:

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    2. 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.
    3. 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.

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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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