This work on univariate and Vector Autocorrelation (VAR) time series model for the sectors in Nigeria, aims at providing an in-depth quantitative analysis of the variables (Agriculture, Industry, Building & Construction, Wholesale & Retail trade and Services). The study made use of secondary data, of all the variables investigated in the model, collected from the National Bureau of Statistics’ Statistical Bulletin (2018). The sample covers quarterly data from 1981 to 2018. Univariate and Multivariate time series estimation techniques – Autoregressive Integrated Moving Average (ARIMA) and Vector Autoregressive (VAR) were employed. Plots of the five sectors indicate that they all have Quadratic trend with appreciation and depreciation. Correlation analysis of the data set show that there exists a strong relationship among each variable. Each of the economic variables ARIMA model was built using Minitab 18 statistical software. Vector autoregressive (VAR) model was also obtained using Gretl statistical software. Two model selection criteria (AIC and BIC) were used to identify and select the suitable models. The identified ARIMA and VAR (2) models were used to make forecasts for the next 6 years for each of the variables. Furthermore, forecast accuracy measure and coefficient of variation (CV) were used to compare and identify the best model to forecast each of the variable. The result confirm that the best model to forecast the Agriculture and Building/Construction variables is the VAR(2) model; while Industry, Wholesale/Retail and Services variables was the ARIMA model [ARIMA(2,1,1)(1,1,1)4, ARIMA(2,1,1)(1,1,1)4and ARIMA(1,1,1)(1,1,1)4].