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The Covariance Structure of Mixed ARMA Models

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  • Menelaos Karanasos

Abstract

This paper extents Karanasos (1999a) results for the n Component GARCH(1,1) and the two Component GARCH(2,2) models and it further examines the n Component GARCH(n,n) model. In particular, we present the GARCH(n^2;n^2) representation of the aggregate variance and we give the condition for the existence of the fourth moment of the errors. In addition, we use the canonical factorization of the autocovariance generating function for the univariate ARMA representations of the component variances, the aggregate variance and the squared errors to obtain their autocovariances and cross covariances. Finally, we illustrate our general results giving three examples: the three component GARCH(1,1), the two component GARCH(2,2) and the three component GARCH(2,2) models.

Suggested Citation

  • Menelaos Karanasos, "undated". "The Covariance Structure of Mixed ARMA Models," Discussion Papers 00/11, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:00/11
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    References listed on IDEAS

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    1. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
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    3. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083, April.
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    5. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    6. Menelaos Karanasos, "undated". "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
    7. 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.
    8. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
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    10. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
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    12. Mittnik, Stefan, 1987. "Non-recursive methods for computing the coefficients of the autoregressive and the moving-average representation of mixed ARMA processes," Economics Letters, Elsevier, vol. 23(3), pages 279-284.
    13. Changli He & Timo Terasvirta & Hans Malmsten, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," Research Paper Series 29, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, "undated". "Cross-Sectional Aggregation and Persistence in Conditional Variance," Discussion Papers 00/09, Department of Economics, University of York.
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    Cited by:

    1. Paulina Granados Z., 2004. "Income Function of Chilean Households: Life Cicle and Persistence of Shocks," Working Papers Central Bank of Chile 257, Central Bank of Chile.
    2. Paulina Granados Z., 2004. "Función de Ingresos de los Hogares Chilenos: Ciclo de vida y Persistencia de Shocks," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 7(1), pages 51-89, April.

    More about this item

    Keywords

    Persistence in Volatility; Component-GARCH; ARMA Representations; Autocovariance Generating Function.;

    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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