A Multivariate GARCH Model with Time-Varying Correlations

30 Pages Posted: 11 Dec 2000

See all articles by Yiu Kuen Tse

Yiu Kuen Tse

Singapore Management University - School of Social Sciences

Albert K.C. Tsui

National University of Singapore (NUS) - Department of Economics

Date Written: November 2000

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.

Keywords: BEKK model, constant correlation, Monte Carlo method, multivariate GARCH model, maximum likelihood estimate, varying correlation

JEL Classification: C12

Suggested Citation

Tse, Yiu Kuen and Tsui, Albert K.C., A Multivariate GARCH Model with Time-Varying Correlations (November 2000). Available at SSRN: https://ssrn.com/abstract=250228 or http://dx.doi.org/10.2139/ssrn.250228

Yiu Kuen Tse (Contact Author)

Singapore Management University - School of Social Sciences ( email )

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Albert K.C. Tsui

National University of Singapore (NUS) - Department of Economics ( email )

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Singapore 117570, Singapore 119077
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