Bank stocks have been considered to be lucrative equity investments in Stock exchanges operating in Pakistan, over the recent time period. Sudden fluctuations in stock prices within a short period have always been a matter of great concern for investors. Since, investors want to take care of advantage they potentially yield from the organization by means of investing in shares; therefore, they tend to be keenly interested in making predictions about their future prices so that their objective of wealth maximization can be achieved. This motive makes forecasting of stocks an interesting topic to be explored empirically. This brought the motivation to study a sample of five big banks (known as Big Five) of Pakistan for predicting their stock prices. The data of stock prices for selected banks has been collected over about a decade from the official website of Karachi Stock Exchange (KSE). For prediction of stocks, moving average, exponential smoothing, time series regression etc. are the most commonly used linear methods. Out of them, the most renowned and widely used linear method is Autoregressive Integrated Moving Average (ARIMA), also known as Box-Jenkins’s Technique. It was proposed by Box and Jenkins in 1976. Despite of being a linear method, it is more flexible in terms of representing various versions of time series as such Autoregressive (AR), Moving Average (MA), combined AR and MA series (ARIMA). Findings revealed that MCB and BOP has found to have maximum number of observations while HBL in this regard, ranking lowest in the group. Distributions of all stocks are found positively skewed while distribution of stocks of each bank is non-normally distributed which may be evident from Jarque–Bera test. Since values of stocks of our sample banks are found highly fluctuated, probably, due to some specific trend, therefore, to predict the future values of stocks, different ARIMA models have been developed here by using Box-Jenkins approach. Accordingly, after identification, estimation, and application of various diagnostic checks, ARIMA(1,1,0) was found to be suitable for prediction of stock of ABL, HBL and MCB. On the other hand, ARIMA(1,1,1) was found to be appropriate for BOP and UBL stocks’ prediction. To address the issue of uncertainty and underlying risk present in securities investments, present study is highly significant for the prospective investors to decide as to which bank they should consider for investment thereby making their expected returns realize.