Implementation of genetic algorithm in model identification of box-jenkins methodology

Abstract

During the past several decades, a considerable amount of studies have been carried out on time series and in particular the Box-Jenkins (BJ) method. As with all techniques of statistical analysis, the conclusions of time series analysis are critically dependent on the assumptions underlying the analysis and BJ is a commonly used forecasting method that can yield highly accurate forecasts for certain types of data. Genetic Algorithm (GA) is a heuristic method of optimization. This study presents the study on developing an extrapolative BJ model with the use of GA method to produce forecasting models using time series data. BJ method has a cycle of four phases, the data transformation phase for model identification, parameter estimation, model diagnostic checking or validation, and finally producing the forecast. Although many researchers and practitioners have concentrated in the parameter estimation part of BJ model, the most crucial stage in building the model is in the data transformation and model identification where any false identification will lead to assuming a wrong model and will increase in the cost of reidentification. Hence, using GA a subset of artificial intelligence methods was introduced into the process of BJ to solve the problem in the model identification and parameter estimation phase. The data used in this study are the monthly data of international tourists arrival into Malaysia from 1990 to 2011. This is a case study in the implementation of GA-BJ model. The result from this study may be divided into two main parts, namely the result for the in-sample data (fitted model) and outsample data (forecast model). The analysis shows that the out-sample values using GA-BJ model gives better forecast accuracy than the out-sample values for BJ model. This shows that the combination of BJ and GA methods gives a more accurate model than using a single method for forecasting. This study concludes that GA method can be an alternative way in identifying the right order of component in BJ model.