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Some Exact Formulae for the Constant Correlation and Diagonal M - Garch Models

  • Menelaos Karanasos

The purpose of this paper is to examine the covariance structure of multivariate GARCH (M-GARCH) models that have been introduced in the literature the last fifteen years, and have been greatly favoured by time series analysts and econometricians. In particular, we analyze the second moments of the constant conditional correlation M-GARCH model introduced by Bollerslev (1990) and the diagonal M-GARCH model introduced by Bollerslev, Engle and Wooldridge (1988).

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 00/14.

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Handle: RePEc:yor:yorken:00/14
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  1. Stephen G. Cecchetti & Robert E. Cumby & Stephen Figlewski, 1986. "Estimation of the optimal futures hedge," Research Working Paper 86-10, Federal Reserve Bank of Kansas City.
  2. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  3. 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.
  4. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, . "Cross-Sectional Aggregation and Persistence in Conditional Variance," Discussion Papers 00/09, Department of Economics, University of York.
  5. G. William Schwert & Paul J. Seguin, 1989. "Heteroskedasticity in Stock Returns," NBER Working Papers 2956, National Bureau of Economic Research, Inc.
  6. 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.
  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.
  8. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  9. 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.
  10. 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.
  11. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  12. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  13. 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).
  14. Karolyi, G Andrew, 1995. "A Multivariate GARCH Model of International Transmissions of Stock Returns and Volatility: The Case of the United States and Canada," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 11-25, January.
  15. 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.
  16. 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.
  17. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  18. 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.
  19. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  20. Stilianos Fountas & Menelaos Karanasos & Marika Karanassou, 2000. "A GARCH Model of Inflation and Inflation Uncertainty with Simultaneous Feedback," Working Papers 0047, National University of Ireland Galway, Department of Economics, revised 2000.
  21. Menelaos Karanasos, . "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
  22. Thomas H. McCurdy & Ieuan G. Morgan, 1991. "Tests for a Systematic Risk Component in Deviations From Uncovered Interest Rate Parity," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 587-602.
  23. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  24. 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.
  25. 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.
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