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A Multivariate GARCH Model with Time-Varying Correlations

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Author Info
Yiu Kuen Tse (National University of Singapore)
Albert K. C. Tsui (National University of Singapore)

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Abstract

In this paper we propose a new multivariate GARCH model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By imposing some suitable restrictions on the conditional-correlation-matrix equation, we manage to construct a MGARCH model in which the conditional-correlation matrix is guaranteed to be positive definite during the optimisation. Thus, our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and BEKK models. We report some Monte Carlo results on the finite-sample distributions of the QMLE of the varying-correlation MGARCH model. The new model is applied to some real data sets. It is found that extending the constant-correlation model to allow for time-varying correlations provides some interesting time histories that are not available in a constant-correlation model.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0250.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0250

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  2. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237. [Downloadable!] (restricted)
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  3. Kroner, Kenneth F. & Claessens, Stijn, 1991. "Optimal dynamic hedging portfolios and the currency composition of external debt," Journal of International Money and Finance, Elsevier, vol. 10(1), pages 131-148, March. [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)
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  5. 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)
  6. 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.
  7. 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!]
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  8. Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2000. "A New Approach to Measuring Financial Contagion," NBER Working Papers 7913, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. 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)
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  12. 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)
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  14. Robert F. Engle & David F. Hendry & David Trumble, 1985. "Small-Sample Properties of ARCH Estimators and Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 66-93, February. [Downloadable!] (restricted)
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  19. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September. [Downloadable!] (restricted)
  20. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January. [Downloadable!] (restricted)
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