GARCH Models and Distributions Comparison for Nonlinear Time Series with Volatilities

Abstract

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is extensively used for handling volatilities. However, with numerous extensions to  the standard GARCH model, selecting the most suitable model for forecasting price volatilities becomes challenging. This study aims to examine the performance of different GARCH models in forecasting crude oil price volatilities using West Texas Intermediate (WTI) data. The models considered are the standard GARCH, Integrated GARCH (IGARCH), Exponential GARCH (EGARCH), and Golsten, Jagannathan, and Runkle GARCH (GJR-GARCH), each with normal distribution, Student’s t-distribution, and Generalized Error Distribution (GED). To evaluate the performance of each model, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used as the model selection criteria, along with forecast accuracy measures such as absolute error, root mean squared error (RMSE), and mean absolute error (MAE). Post-estimation tests, including the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test and the Ljung-Box test, are conducted to ensure the adequacy of all models. The results reveal that all GARCH models are suitable for modeling the data, as indicated by statistically significant estimated parameters and satisfactory post-estimation outcomes. However, the EGARCH (1, 1) model, particularly with Student’s t-distribution, outperforms other models in both data fitting and accurate forecasting of nonlinear time series.