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A Multivariate GARCH Model with Time-Varying correlations

Author

Listed:
  • Y. K. 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 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 MLE 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

  • Y. K. Tse & Albert K. C. Tsui, 2000. "A Multivariate GARCH Model with Time-Varying correlations," Econometrics 0004010, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0004010
    Note: Type of Document - PDF; prepared on PC; to print on Postscript; pages: 30; figures: included
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    More about this item

    Keywords

    BEKK model; constant correlation; Monte Carlo method; multivariate GARCH model; maximum likelihood estimate; varying correlation;

    JEL classification:

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

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