Shares or stocks are forms of financial securities that are vital in funding corporate operations and expenses. This project aims at analyzing NSE 20 share index from the year 2001 to 2018 in order to create a price prediction and forecasting model. Methods involved include time series univariate models such as Auto-correlation, regression, Dickey –Fuller test, ARIMA and test on residuals. Results and conclusion proves this model to have 72% efficiency in the prediction of future share index prices hence giving a vote of confidence that it can be used by investors to trade their shares.