Analysis of dependence structure between the Rand/U.S Dollar exchange rate and the gold/platinum prices

Abstract

Copulas functions are a flexible tool for modelling the dependence structure between variables. The joint and marginal distributions of Copulas are not constrained by the assumptions of normality. This study examines the dependence structure between the gold, platinum prices and the ZAR/U.S.D exchange rate using Copulas. The study found that marginal distributions of Copulas follows the ARMA (1, 1)-EGARCH (1, 1) and ARMA(1, 1)-APARCH (1, 1) models under different error terms including the normal, the student-t and the skew student-t error terms. It used the Normal, the Student-t, the Gumbel, the rotated Gumbel, the Clayton, the rotated Clayton, the Plackett, the Joe Clayton and the Normal time varying Copulas to analyse the dependence structure between returns prices of gold, platinum and ZAR/U.S.D exchange rate. The results showed evidence of a positive strong dependence between the returns prices of gold, platinum and returns on the Rand/U.S.D exchange rate for constant and time varying Copulas. The result also showed a co-movement of exchange rates and gold and platinum prices during a rise or declining prices of gold and platinum. The results imply that fluctuations in gold and platinum prices generate Rand/U.S.D exchange rate volatility.