Equity Return Modeling and Prediction Using Hybrid ARIMA-GARCH Model

Abstract

In this paper, a hybrid ARIMA-GARCH model is proposed to model and predict the equity returns for three US benchmark indices: Dow Transportation, S&P 500 and VIX. Equity returns are univariate time series data sets, one of the methods to predict them is using the Auto-Regressive Integrated Moving Average (ARIMA) models. Despite the fact that the ARIMA models are powerful and flexible, they are not be able to handle the volatility and nonlinearity that are present in the time series data. However, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models are designed to capture volatility clustering behavior in time series. In this paper, we provide motivations and descriptions of the hybrid ARIMA-GARCH model. A complete data analysis procedure that involves a series of hypothesis testings and a model fitting procedure using the Akaike Information Criterion (AIC) is provided in this paper as well. Simulation results of out of sample predictions are also provided in this paper as a reference.