Parameter estimation of box-jenkins model using genetic algorithm

Abstract

Malaysia is very fortunate to be free from natural disaster such as earth quake, volcano and typhoon. Unfortunately, the most severe natural disaster experiencing in Malaysia is flood. The probability of flood may occur had been increase due to the climate change and global warming that happened in Malaysia throughout the year. One of the major factor that contribute to flood is the heavy rainfall or maximum rainfall. Hence, in this study, mathematical analysis had been performed by studying the rainfall pattern of the past years and predict the future pattern. Ulu Sebol station situated in Johor was chosen as the rainfall data station since Johor is one of the state that experienced the worst flood in the year 2006. Accuracy plays an important role in choosing the forecasting techniques in order to make prediction of the future rainfall data. But, before forecasting can be made, estimation of the model parameter must be done. In this thesis, an approach that combines the Box-Jenkins methodology for ARIMA model and Genetic Algorithm (GA) had been introduced as a new approach in estimating the parameter and forecasting. A total of 127 series of data had been used in this study starting from January 2000 and these data were classified as monthly maximum rainfall data. MINITAB 16 computer package was used in analyzing the data and for the development of Box-Jenkins model. Meanwhile, JAVA was used in estimating the parameter of Box-Jenkins model by using Genetic Algorithm. The accuracy of the results were measured by concerning the minimum Mean Absolute Percentage Error (MAPE). By using MINITAB 16, ARIMA(0,1,1) was chosen as the best model that fits to the data. The best estimate of theta given by MINITAB is � = 0.9857 with MAPE 0.6526. By adopting GA in searching the best parameter value, GA gives an outstanding performance with the best estimate of theta is 0.3427 and MAPE with 0.5416. Hence, Genetic Algorithm was proven to work well in estimating the parameter of Box-Jenkins model.