A Multivariate Threshold GARCH Model with Time-varying Correlations

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Heteroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) in a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Extension of Bollerslev, Engle and Wooldridge (1988) in a threshold framework is also proposed as a by-product. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the VCMTGARCH model. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and that the VC-MTGARCH model can capture these phenomena. Email: [email protected]. Department of Applied Mathematics, The Hong Kong Polytechnic University and Department of Statistics and Actuarial Science, The University of Hong Kong. Email: [email protected]. Department of Statistics and Actuarial Science, The University of Hong Kong Email: [email protected] Department of Statistics and Actuarial Science, The University of Hong Kong 1