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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 MSEs are presented. We also derive the formula for the covariance structure of the process and its conditional variance. JEL. C22.

Suggested Citation

  • Menelaos Karanasos, 2001. "Prediction in ARMA Models with GARCH in Mean Effects," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 555-576, September.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:5:p:555-576
    DOI: 10.1111/1467-9892.00241
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. repec:awi:wpaper:0473 is not listed on IDEAS
    4. 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.
    5. 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.
    6. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    7. 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.
    8. Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2021. "Analytic moments for GJR-GARCH (1, 1) processes," International Journal of Forecasting, Elsevier, vol. 37(1), pages 105-124.
    9. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
    10. 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.
    11. 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.
    12. 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).
    13. 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.
    14. 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.

    More about this item

    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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