Estimating, Forecasting and Backtesting a Family of Exponential and Other GARCH Models Using the fEGarch Package

A new R package called fEGarch is introduced that allows for the estimation of a broad family of short- and long-memory EGARCH models, as well as other popular short- and long-memory GARCH-type models, such as the (FI)GARCH and (FI)APARCH models. The EGARCH-family includes the well-established EGARCH and FIEGARCH models as special cases. An overview of the EGARCHfamily models, their semiparametric extension and their extension to dual models with simultaneous mean modelling is given. Backtesting strategies for valueat- risk and expected shortfall in this context are summarized. A practical comparison with the rugarch package is drawn based on EGARCH models and the package’s capabilities are compared to those of OxMetrics and the R package ufRisk. A simulation study highlights the consistency of the fEGarch estimators for the EGARCH-family models and their applications to real-world log-returns from stock markets underline the models’ convincing performance. The application of fEGarch for backtesting multivariate GARCH and non-GARCH volatility models is presented briefly. The appendix includes relevant theoretical information, such as on available conditional distributions, including the new (scaled) average Laplace distribution and its skewed variant, as well as on estimation via conditional QMLE and on value-at-risk and expected shortfall forecasting.