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fEGarch: SM/LM EGARCH & GARCH, VaR/ES Backtesting & Dual LM Extensions

Implement and fit a variety of short-memory (SM) and long-memory (LM) models from a very broad family of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models, such as a MEGARCH (modified EGARCH), FIEGARCH (fractionally integrated EGARCH), FIMLog-GARCH (fractionally integrated modulus Log-GARCH), and more. The FIMLog-GARCH as part of the EGARCH family is discussed in Feng et al. (2023) <https://econpapers.repec.org/paper/pdnciepap/156.htm>. For convenience and the purpose of comparison, a variety of other popular SM and LM GARCH-type models, like an APARCH model, a fractionally integrated APARCH (FIAPARCH) model, standard GARCH and fractionally integrated GARCH (FIGARCH) models, GJR-GARCH and FIGJR-GARCH models, TGARCH and FITGARCH models, are implemented as well as dual models with simultaneous modelling of the mean, including dual long-memory models with a fractionally integrated autoregressive moving average (FARIMA) model in the mean and a long-memory model in the variance, and semiparametric volatility model extensions. Parametric models and parametric model parts are fitted through quasi-maximum-likelihood estimation. Furthermore, common forecasting and backtesting functions for value-at-risk (VaR) and expected shortfall (ES) based on the package's models are provided.

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