Macroeconomic variables are the main signposts signaling the current trends in an economy. In this study, data on the 91-day T-bill rate, 182-day T-bill rate, inflation rate and exchange rate from the Bank of Ghana database was modelled using multivariate time series techniques to investigate the dynamic interrelationships existing between these macroeconomic variables over time. The results revealed that, the 91-day T-bill, 182-day T-bill and inflation rates exhibit log-quadratic trends whiles exchange rate exhibit log-linear trend. Results of the Johansen's unrestricted trend co-integration test performed revealed that, the four set of variables were co-integrated and two linearly independent co-integrating equations describe the long run equilibrium relationship between these variables over time. The results also revealed that, both VAR (1) and VEC (2) models fitted was structural stable over time and best described the short run relationship between the rates over time. However, for a further inference on the relationship between the four time series variables, the VAR (1) model was selected since it has the least AIC, SBIC, HQIC and the maximum likelihood ratio values.