This work focused on method of modeling multivariate time series with seasonal univariate components. Five variables representing Nigeria’s Gross Domestic Products (GDP) were found to exhibit seasonal behaviours. These series were subjected to Box and Jenkins techniques and different univariate seasonal models were entertained for each component. The residuals from the fitted univariate models were cross examined. The correlation and cross correlation structures of these residuals revealed the inter-relationships among the variables, and multivariate consideration was therefore obvious. Multivariate order selection technique was employed to obtain the vector autoregressive (VAR) order of the model. A VAR (1) model was identified and developed to fit the data. Stability of the VAR process was achieved. Diagnostic checks were applied to the fitted model and the model was found to be adequate. Hence, forecasts were generated.