A Multivariate GARCH Model with Time-Varying Correlations
AbstractIn 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.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0004007.
Length: 30 pages
Date of creation: 06 Nov 2000
Date of revision:
Note: Type of Document - Acrobat PDF; prepared on SW2.5; to print on HP/PostScript/Franciscan monk; pages: 30; figures: included
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BEKK models; constant correlation; Monte Carlo method; multivariate GARCH model; maximum likelihood estimate; varying correlation;
Other versions of this item:
- Y. K. Tse & Albert K. C. Tsui, 2000. "A Multivariate GARCH Model with Time-Varying correlations," Econometrics 0004010, EconWPA.
- 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.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-02-14 (All new papers)
- NEP-ECM-2001-02-14 (Econometrics)
- NEP-ETS-2001-02-14 (Econometric Time Series)
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