G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models

This paper discusses and documents G@RCH 2.2, an Ox package dedicated to the estimation and forecast of various univariate ARCH–type models including GARCH, EGARCH, GJR, APARCH, IGARCH, FIGARCH, HYGARCH, FIEGARCH and FIAPARCH specifications of the conditional variance and an AR(FI)MA specification of the conditional mean. These models can be estimated by Approximate (Quasi) Maximum Likelihood under four assumptions: normal, Student–t, GED or skewed Student errors. Explanatory variables can enter both the conditional mean and the conditional variance equations. h–step–ahead forecasts of both the conditional mean and the conditional variance are available as well as many mispecification tests. We first propose an overview of the package’s features, with the presentation of the different specifications of the conditional mean and conditional variance. Then further explanations are given about the estimation methods. Measures of the accuracy of the procedures are also given and the GARCH features provided by G@RCH are compared with those of nine other econometric softwares. Finally, a concrete application of G@RCH 2.2 is provided.