factor. In this sense, the estimation of Equation (2) is reduced to individual countries correlation. With the dynamic correlation, a positive correlation should indicate that a country’s market is integrated to a certain extent with the regional (global) market, while the correlation of 1.00 shows full integration. A negative correlation should indicate segmentation or decoupling between countries and their respective trading bloc. The estimation of the DCC-GARCH model follows thus: firstly, a mean equation is estimated as: + (3) with and is a 2-variable vector containing the country exchange return and the specific regional common factor. Xt represents the vectors of deterministic and exogenous variables and the residual combines the white noise process and the heteroscedastic component. Parameters , and need to be estimated. Secondly, the residuals obtained from Equation 3 in the first stage is used as an input into the univariate conditional-variance model specified for the country and common factors stock exchange returns, respectively. To account for possible equity-market asymmetry, we use the Glosten, Jagannathan and Runkle (GJR) (1993) GARCH model, which accounts for the asymmetric effect of stock exchange market returns. The GJR GARCH (1,1) model is represented as follows: (4) where the parameter refers to the long-term conditional variance and is the lag coefficient. is ω α an indicator variable that takes the value of 1 when and zero otherwise. Thus, the impact of on is for negative shocks and for positive shocks. The last in a DCC GARCH model consists of determining the time-variant conditional correlation matrix from the conditional variance expressed as: (5) Where is the diagonal matrix of conditional variances such as =diag . Rt is a positive definite N x N correlation matrix and is defined as follows:
factor. In this sense, the estimation of Equation (2) is reduced to individual countries correlation. With the dynamic correlation, a positive correlation should indicate that a country’s market is integrated to a certain extent with the regional (global) market, while the correlation of 1.00 shows full integration. A negative correlation should indicate segmentation or decoupling between countries and their respective trading bloc. The estimation of the DCC-GARCH model follows thus: firstly, a mean equation is estimated as: + (3) with and is a 2-variable vector containing the country exchange return and the specific regional common factor. Xt represents the vectors of deterministic and exogenous variables and the residual combines the white noise process and the heteroscedastic component. Parameters , and need to be estimated. Secondly, the residuals obtained from Equation 3 in the first stage is used as an input into the univariate conditional-variance model specified for the country and common factors stock exchange returns, respectively. To account for possible equity-market asymmetry, we use the Glosten, Jagannathan and Runkle (GJR) (1993) GARCH model, which accounts for the asymmetric effect of stock exchange market returns. The GJR GARCH (1,1) model is represented as follows: (4) where the parameter ω refers to the long-term conditional variance and α is the lag coefficient. is an indicator variable that takes the value of 1 when and zero otherwise. Thus, the impact of on is for negative shocks and for positive shocks. The last in a DCC GARCH model consists of determining the time-variant conditional correlation matrix from the conditional variance expressed as: (5) Where is the diagonal matrix of conditional variances such as =diag . Rt is a positive definite N x N correlation matrix and is defined as follows: