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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 Quasi-Maximum Likelihood Estimator (QMLE) of 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, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
    • Handle: RePEc:eee:econom:v:194:y:2016:i:2:p:319-329
    DOI: 10.1016/j.jeconom.2016.05.010
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    Cited by:

    1. 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.
    2. 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.
    3. Dias, Gustavo Fruet, 2017. "The time-varying GARCH-in-mean model," Economics Letters, Elsevier, vol. 157(C), pages 129-132.
    4. 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.
    5. 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.
    6. Perera, Indeewara & Silvapulle, Mervyn J., 2023. "Bootstrap specification tests for dynamic conditional distribution models," Journal of Econometrics, Elsevier, vol. 235(2), pages 949-971.
    7. 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.
    8. Asai, Manabu, 2023. "Feasible Panel GARCH Models: Variance-Targeting Estimation and Empirical Application," Econometrics and Statistics, Elsevier, vol. 25(C), pages 23-38.

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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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