Comparative Performance of ARIMA and ARCH/GARCH Models on Time Series of Traffic Accidents in Gaza Strip

Abstract

The accuracy of forecasts using time series models has recently received a great attention. The Box-Jenkins, SARIMA models have been the most widely used models for forecasting. These models give good forecasts for future observations but they are not so accurate for many ones. Recent studies suggest that GARCH models which take into account volatility in the time series can be a promising alternative to the traditional method SARIMA in forecasting especially in the case of non-linear data and for forecasting many future forecast values. The aim of this study is to evaluate the performance of SARIMA as linear models and GARCH as non-linear models to forecast monthly Traffic Accident number in Gaza-Strip. This study used the Box-Jenkins methodology and GARCH approach in analysing the Traffic Accident data. We consider multiple time series models for fitting our data for the period from 1st January 1995 to 31st December 2014, The data are divided into two parts. One is for model’s estimation and another is for tasting purposes. We selected the best SARIMA models and the best GARCH model based on model selection criteria AIC, AICc and BIC, then we made a comparison between SARIMA(3; 1; 2)(1; 0; 1)12 and ARMA(1; 1)-GARCH(1; 1) models in order to determine which better to use in similar situation. The analysis of this study are carried out with the assist of R software. The accuracy of GARCH and SARIMA models for forecasting monthly Traffic Accidents in Gaza Strip was compared using different statistical forecast evaluation criteria MAE, MSE, RMSE and MAPE efficiency between SARIMA(3; 1; 2)(1; 0; 1)12 and ARMA(1; 1)-GARCH(1; 1) model, we found that nonlinear models outperform linear models and ARMA(1; 1)-GARCH(1; 1) outperforms SARIMA(3; 1; 2)(1; 0; 1)12 model.