Box-Jenkins Approach for Out-of-Sample Forecasting of Stock Price Index: Evidence from Colombo Stock Exchange

Abstract

Univariate time series analysis under the time domain has become a widely used data analysis technique from the past. The methods belong to time series could be used to identify the temporal structure of data and forecasting. Among them Box and Jenkins approach has been used in the research studies and could be rendered as the commonly used method. Accordingly, they have introduced a model to predict the future behaviour through an auto-projective method that uses the past behaviour of the series. The purpose of this study is to obtain accurate out-of-sample forecasts for stock price indices using an ARIMA model. The daily All Share Price Indices (ASPI) were used over the period from 2nd January 2012 to 31st December 2013 in Colombo Stock Exchange (CSE), Sri Lanka. This study used Box-Jenkins method with four main concepts of model identification, estimation, diagnostic checking and forecasting. Basically, the concept of information criteria was used for the model identification process. The corresponding model Parameters were estimated at the training data sample using the least square method. Moreover, residual plots and residual tests were used to check the model diagnosis. Finally, different error approaches such as mean absolute error (MAE), root mean square error (RMSE), and mean absolute percent error (MAPE) were used to evaluate the forecast performances of the selected models through different time horizons. Two models were chosen according to the results of Akaike's information criterion (AIC), Schwarz's Bayesian information criterion (SBIC), and Hannan-Quinn criterion (HQIC.) The out-of-sample forecasting indicates that the selected two models are appropriate for one step ahead forecasting than the long time horizon. The aggregate results depicted that; ARMA (1, 1, 0) is the optimal model and can produce more accurate result than ARIMA (4, 1, 5) for ASPI data within the considered time period.