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Volatile ARMA Modelling of GARCH Squares

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  • Anthony J. Lawrance

    ()
    (University of Warwick)

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    Abstract

    This paper points out that the ARMA models followed by GARCH squares are volatile and gives explicit and general forms of their dependent and volatile innovations. The volatility function of the ARMA innovations is shown to be the square of the corresponding GARCH volatility function. The prediction of GARCH squares is facilitated by the ARMA structure and predictive intervals are considered. Further, the developments suggest families of volatile ARMA processes.

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    File URL: http://cejeme.eu/publishedarticles/2011-16-23-634576797730000000-4494.pdf
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    Bibliographic Info

    Article provided by CEJEME in its journal Central European Journal of Economic Modelling and Econometrics.

    Volume (Year): 2 (2010)
    Issue (Month): 3 (June)
    Pages: 195-203

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    Handle: RePEc:psc:journl:v:2:y:2010:i:3:p:195-203

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    Web page: http://cejeme.org/

    Related research

    Keywords: ARCH; ARMA; GARCH; prediction; time series; volatility;

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    1. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    2. Shiqing Ling, 2004. "Estimation and testing stationarity for double-autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78.
    3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
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