The stock market is basically volatile, and the prediction of its movement will be more useful to the stock traders to design their trading strategies. An intelligent forecasting will certainly abet to yield significant profits. Many important models have been proposed in the economics and finance literature for improving the prediction accuracy, and this task has been carried out through modelling based on time-series analysis. The main aim of this paper was to check the stationarity in time series data and predicting the direction of change in stock market index using the stochastic time series ARIMA modelling. The best fit ARIMA (0,1,0) model was chosen for forecasting the values of time series, that is, BSE_CLOSE and NSE_CLOSE by considering the smallest values of AIC, BIC, RMSE, MAE, MAPE, standard error of regression, and the relatively high adjusted R2 values. Using this best fitted model, the predictions were made for the period ranging from January 7, 2018 to June 3, 2018 (22 expected values) using the weekly data ranging from January 6, 2014 to December 31, 2017 (187 observed values). The results obtained from the study confirmed the prospectives of ARIMA model to forecast the future time series in short-run and would assist the investing community in making profitable investment decisions.