© 2020 Scholars Journal of Physics, Mathematics and Statistics | Published by SAS Publishers, India 110 Scholars Journal of Physics, Mathematics and Statistics Abbreviated Key Title: Sch J Phys Math Stat ISSN 2393-8056 (Print) | ISSN 2393-8064 (Online) Journal homepage: https://saspublishers.com/sjpms/ Application of Box – Jenkins ARIMA (p, d, q) Model for Stock Price Forecasting and Detect Trend of S&P BSE Stock Index: An Evidence from Bombay Stock Exchange Rahul Kumar Si 1* , Shishir Kumar Padhan 2 , Dr. Bidyadhara Bishi 3 1 Statistical Assistant, Tobacco Board, Ministry of Commerce & Industry, Govt. of India, Guntur, Andhra Pradesh – 522004, India 2 Senior Statistical Officer, NSO (FOD), Ministry of Statistics & PI, Govt. of India, Vellore, Tamil Nadu - 632009, India 3 Research Scholar, P.G. Department of Statistics, Sambalpur University, Jyotivihar, Burla, Sambalpur, Odisha – 768019, India DOI: 10.36347/sjpms.2020.v07i07.006 | Received: 14.07.2020 | Accepted: 22.07.2020 | Published: 30.07.2020 *Corresponding author: Rahul Kumar Si Abstract Original Research Article STOCK price prediction is an important topic in financial statistics which stimulates the interest over the years to develop better predictive models. It also provides a way to predict and perhaps avoid the risk of large adverse changes in price. Autoregressive Integrated Moving Average (ARIMA) methodology: “A real time risk prediction technique, flexible in computing and universal approximate because of its simplicity and wide acceptability that can be applied to a wide range of forecasting problems with a high degree of accuracy for the convenience of predicting the future value in share market and gives a better future scope for investment” is used in this paper to forecast the S&P BSE stock price. Before forecasting the stock prices using ARIMA model, a trend analysis was conducted on the sample data to find out the nature of the time series, i.e. upward trend, stationary or downward trend. The skewness and kurtosis also give the basic idea about the shape of the time series data. Augmented Dickey – Fuller (ADF) and Phillips – Perron (PP) unit root test were applied to know about the stationarity of the time series data. A robust model was identified by comparing the smallest value of Akaike‟s Information Criteria (AIC) and Bayesian Information Criteria (B IC). The parameters: R-Square, Adjusted R-Square, S.E of regression and Durbin-Watson statistic were estimated to regulate best ARIMA model. After parameter estimation is done, it is necessary to verify the satisfactoriness of the estimated model. The value of serial correlation was studied to verify that the series of correlation residuals is white noise or not. After the speculative model has been fitted, Ljung-Box Q statistic was applied for diagnostic checking or suitability of the model. Forecasting is the next step of the ARIMA model, which is an essential part of time series analysis. It is the predicted values based on identified past values of that variable or other related variable. Mean Absolute Percentage Error (MAPE) was calculated to determine the forecast accuracy as well as performance of the model. Keywords: Stock, Forecast, ARIMA, Correlogram, Ljung-Box Q statistic and MAPE. Copyright @ 2020: This is an open-access article distributed under the terms of the Creative Commons Attribution license which permits unrestricted use, distribution, and reproduction in any medium for non-commercial use (NonCommercial, or CC-BY-NC) provided the original author and source are credited. INTRODUCTION A stock is a share in the aspiration of a company. It represents the claim on the company‟s assets and incomes. It is also known as equity of share and a portion of the ownership in a corporate sector by an indivisual. Hence, a stock of a company entitles its share holders in its profit and issuing shares by a corporate company can mobilize huge capitals. Most of these shares are traded in exchanges, where buyers and sellers will meet and make a decision on a price is called „Stock Market‟. It is the aggregation of buyers and sellers of stocks and represents the ownership of a business. Transaction in stock market means the transfer of money from a seller to buyer for equities when they agree on a certain price and is facilitated by a stock exchange. Stock market is a place where investors, whether Indians or foreigners can invest or take their funds for capital appreciation. Their decision to invest or withdraw the funds depends upon the numerous factors. For this cause Indian stock market plays a significant role in the growth of Indian economy and every movement on it puts an impact on the performance of the economy. The Indian stock market had seen various up- down since 1991, after the government implemented the LPG, i.e., Liberalization, Privatization and