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Prediction in ARMA models with GARCH in Mean Effects

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  • Menelaos Karanasos

Abstract

This paper considers forecasting the conditional mean and variance from an ARMA model with GARCH in mean effects. Expressions for the optimal predictors and their conditional and unconditional MSE's are presented. We also derive the formula for the covariance structure of the process and its conditional variance.

Suggested Citation

  • Menelaos Karanasos, "undated". "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:99/11
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/1999/9911.pdf
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    References listed on IDEAS

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    1. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    2. Karanasos, M., 1998. "A New Method For Obtaining The Autocovariance Of An Arma Model: An Exact Form Solution," Econometric Theory, Cambridge University Press, vol. 14(5), pages 622-640, October.
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    Cited by:

    1. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    2. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    3. Rong Xu & Xingye Li, 2017. "Study About the Minimum Value at Risk of Stock Index Futures Hedging Applying Exponentially Weighted Moving Average - Generalized Autoregressive Conditional Heteroskedasticity Model," International Journal of Economics and Financial Issues, Econjournals, vol. 7(6), pages 104-110.
    4. Lin, Ling & Jiang, Yong & Xiao, Helu & Zhou, Zhongbao, 2020. "Crude oil price forecasting based on a novel hybrid long memory GARCH-M and wavelet analysis model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).
    5. Menelaos Karanasos, "undated". "The Covariance Structure of Component and Multivariate Garch Models," Discussion Papers 99/12, Department of Economics, University of York.
    6. Menelaos Karanasos, "undated". "Some Exact Formulae for the Constant Correlation and Diagonal M - Garch Models," Discussion Papers 00/14, Department of Economics, University of York.
    7. Menelaos Karanasos, "undated". "The Covariance Structure of Mixed ARMA Models," Discussion Papers 00/10, Department of Economics, University of York.
    8. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.
    9. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    10. Menelaos Karanasos & Alexandros Paraskevopoulos & Faek Menla Ali & Michail Karoglou & Stavroula Yfanti, 2014. "Modelling Returns and Volatilities During Financial Crises: a Time Varying Coefficient Approach," Papers 1403.7179, arXiv.org.
    11. Haiyan Zhao & Fred Huffer & Xu-Feng Niu, 2015. "Time-varying coefficient models with ARMA-GARCH structures for longitudinal data analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 309-326, February.
    12. Stilianos Fountas & Menelaos Karanasos & Marika Karanassou, "undated". "A GARCH Model of Inflation and Inflation Uncertainty with Simultaneous Feedback," Discussion Papers 00/24, Department of Economics, University of York.
    13. Carol Alexander & Emese Lazar & Silvia Stanescu, 2010. "Analytic Moments for GARCH Processes," ICMA Centre Discussion Papers in Finance icma-dp2011-07, Henley Business School, University of Reading, revised Apr 2011.
    14. repec:awi:wpaper:0473 is not listed on IDEAS
    15. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    16. Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009. "Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 330-336, March.
    17. Jaroslava Hlouskova & Kurt Schmidheiny & Martin Wagner, 2002. "Multistep Predictions from Multivariate ARMA-GARCH: Models and their Value for Portfolio Management," Diskussionsschriften dp0212, Universitaet Bern, Departement Volkswirtschaft.
    18. Stilianos Fountas & Menelaos Karanasos & Marika Karanassou, "undated". "A GARCH Model of Inflation and Inflation Uncertainty with Simultaneous Feedback," Discussion Papers 00/24, Department of Economics, University of York.
    19. Menelaos Karanasos & J. Kim, "undated". "Alternative GARCH in Mean Models: An Application to the Korean Stock Market," Discussion Papers 00/25, Department of Economics, University of York.

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    More about this item

    Keywords

    ARMA Model; Conditional Moments; GARCH in Mean Effects;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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