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

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  • Menelaos Karanasos

Abstract

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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File URL: http://www.york.ac.uk/media/economics/documents/discussionpapers/2000/0014.pdf
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Bibliographic Info

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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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Keywords: Autocovariance Generating Function; ARMA representations; Diagonal Multivariate GARCH.;

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  1. Stilianos Fountas & Menelaos Karanasos & Marika Karanassou, . "A GARCH Model of Inflation and Inflation Uncertainty with Simultaneous Feedback," Discussion Papers 00/24, Department of Economics, University of York.
  2. Diebold & Lopez, . "Modeling Volatility Dynamics," Home Pages _062, University of Pennsylvania.
  3. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, . "Cross-Sectional Aggregation and Persistence in Conditional Variance," Discussion Papers 00/09, Department of Economics, University of York.
  4. Menelaos Karanasos, . "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
  5. 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.
  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. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Charles Engel & Anthony P. Rodrigues, 1987. "Tests of International CAPM with Time-Varying Covariances," NBER Working Papers 2303, National Bureau of Economic Research, Inc.
  9. McCurdy, Thomas H & Morgan, Ieuan G, 1991. "Tests for a Systematic Risk Component in Deviations from Uncovered Interest Rate Parity," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 587-602, May.
  10. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  11. 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.
  12. 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.
  13. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  14. Schwert, G William & Seguin, Paul J, 1990. " Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-55, September.
  15. 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.
  16. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
  17. 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.
  18. 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.
  19. 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.
  20. repec:fth:galeco:47 is not listed on IDEAS
  21. 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.
  22. 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).
  23. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  24. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  25. 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.
  26. 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.
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