Modelling and forecasting volatile data by using ARIMA and GARCH models

Abstract

Modelling and forecasting of volatile data have become the area of interest in financial time series. Volatility refers to a condition where the conditional variance changes between extremely high and extremely low values. In the current study, modelling and forecasting will be carried out using two sets of real data namely crude oil prices and kijang emas prices. The models investigated are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model and Generalized Autoregressive Conditionally Heteroscedasticity (GARCH) model. In estimating the parameters for the Box-Jenkins ARIMA model, two estimation methods are used. These are Maximum Likelihood Estimation (MLE) and Ordinary Least Squares Estimation (OLS). The capabilities of these two methods in estimating the ARIMA models are evaluated by using Mean Absolute Percentage Error (MAPE). The modelling performances of ARIMA and GARCH models will be evaluated by using Akaike’s Information Criterion (AIC) while the forecasting performances of both models will be evaluated by using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). The processes of modelling and forecasting will be done by using R and Eviews statistical softwares. As a result of the study, it can be concluded that in terms of parameters estimation of ARIMA models, MLE gives more precise forecast for crude oil prices data while OLS gives more precise forecast for kijang emas prices data. In terms of forecasting performances between ARIMA and GARCH models, it can be concluded that GARCH is a better model for kijang emas prices data while ARIMA is a better model for crude oil prices data.