This paper demonstrates the use of Buys-Ballot table for identification of decomposition model using graphical method, when the trend cycle component is quadratic. A suitable ARIMA model was fitted, and was used for forecasting. Using the Buys-Ballot techniques, the column means, variances and standard deviation were estimated for the model identification. The additive model had no seasonal effect but, the multiplicative model had seasonal effect. The result of the illustrative example using the data of Nigeria Spot component price of oil (US Dollar per Barrel) showed the additive model to be the appropriate model for decomposition of this series. AR(2) model was identified as a suitable ARIMA model for the de-trended Nigeria Spot component price of oil. This was used to make forecast for the next twelve months. The obtained expected oil prices were compared with the observed prices. The comparison of expected and observed prices showed no significance difference between them, using Mean Absolute Percentage Error (MAPE).