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A Multivariate GARCH Model with Time-Varying Correlations

Author

Listed:
  • Yiu Kuen Tse

    (National University of Singapore)

  • Albert K. C. Tsui

    (National University of Singapore)

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.

Suggested Citation

  • Yiu Kuen Tse & Albert K. C. Tsui, 2000. "A Multivariate GARCH Model with Time-Varying Correlations," Econometric Society World Congress 2000 Contributed Papers 0250, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0250
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    References listed on IDEAS

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    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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