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The Covariance Structure of Component and Multivariate Garch Models

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Menelaos Karanasos

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Abstract

The purpose of this paper is to examine the variance-covariance structure of GARCH models that have been introduced in the literature the last decade, and have been greatly favoured by time series analysts and econometricians. In particular, we analyze the second moments of the sum of GARCH models examined in Karanasos, Psaradakis and Sola (1998), the multivariate GARCH models presented by Bollerslev, Engle and Wooldridge (1998) and Bollerslev (1990), the component GARCH models introduced by Ding And Granger (1996) and Karanasos (1998b), and the GARCH-M-X models presented by Longstaff and Schwartz (1992), and Christodoulakis, Hatgioannides and Karanasos (1998).

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 99/12.

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Handle: RePEc:yor:yorken:99/12

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Related research
Keywords: Autocovariances; Multivariate GARCH; N Components; GARCH in mean.;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February. [Downloadable!] (restricted)
  2. Kroner, Kenneth F. & Sultan, Jahangir, 1993. "Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 535-551, December. [Downloadable!]
  3. McCurdy, Thomas H & Morgan, Ieuan G, 1991. "Tests for a Systematic Risk Component in Deviations from Uncovered Interest Rate Parity," Review of Economic Studies, Blackwell Publishing, vol. 58(3), pages 587-602, May. [Downloadable!] (restricted)
  4. Engel, Charles & Rodrigues, Anthony P, 1989. "Tests of International CAPM with Time-Varying Covariances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(2), pages 119-38, April-Jun. [Downloadable!] (restricted)
    Other versions:
  5. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April. [Downloadable!]
    Other versions:
  6. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May. [Downloadable!] (restricted)
  7. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November. [Downloadable!] (restricted)
  8. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Blackwell Publishing, vol. 7(4), pages 305-66, December.
  9. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  10. Cecchetti, Stephen G & Cumby, Robert E & Figlewski, Stephen, 1988. "Estimation of the Optimal Futures Hedge," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 623-30, November. [Downloadable!] (restricted)
    Other versions:
  11. Menelaos Karanasos, . "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York. [Downloadable!]
  12. Diebold & Lopez, . "Modeling Volatility Dynamics," Home Pages _062, University of Pennsylvania. [Downloadable!]
    Other versions:
  13. Baillie, Richard T & Myers, Robert J, 1991. "Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(2), pages 109-24, April-Jun. [Downloadable!] (restricted)
  14. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, . "Cross-Sectional Aggregation and Persistence in Conditional Variance," Discussion Papers 00/09, Department of Economics, University of York. [Downloadable!]
  15. Ng, Lilian, 1991. " Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach," Journal of Finance, American Finance Association, vol. 46(4), pages 1507-21, September. [Downloadable!] (restricted)
  16. Lin, Wen-Ling, 1997. "Impulse Response Function for Conditional Volatility in GARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 15-25, January.
  17. Longstaff, Francis A & Schwartz, Eduardo S, 1992. " Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-82, September. [Downloadable!] (restricted)
  18. McCurdy, T.H. & Morgan, I.G., 1989. "Evidence of risk Premia in Foreign Currency Futures Markets," UFAE and IAE Working Papers 130.90, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. Grier, Kevin B. & Perry, Mark J., 1996. "Inflation, inflation uncertainty, and relative price dispersion: Evidence from bivariate GARCH-M models," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 391-405, October. [Downloadable!] (restricted)
  20. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  21. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February. [Downloadable!]
  22. Schwert, G William & Seguin, Paul J, 1990. " Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-55, September. [Downloadable!] (restricted)
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  23. Baillie, Richard T. & Bollerslev, Tim, 1990. "A multivariate generalized ARCH approach to modeling risk premia in forward foreign exchange rate markets," Journal of International Money and Finance, Elsevier, vol. 9(3), pages 309-324, September. [Downloadable!] (restricted)
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