ARMA-GARCH/APARCH Models with Stable, GEV and GAt Innovations • GEVStableGarch

An R package for ARMA-GARCH and ARMA-APARCH models with stable, GEV (Generalized Extreme Value) and GAt (Generalized Asymmetric t, Paolella 1997) innovations: estimation, simulation, stationarity checks and forecasting (including Value-at-Risk). These three families are not offered by fGarch, rugarch or tsgarch. Useful for financial time series with volatility clustering, heavy tails and skewness.

The innovation distribution is a pluggable object: a user defined density gets the same fitting, simulation, stationarity and forecasting machinery, and the constructor checks that everything it declares is consistent, so fitting never fails silently.

Version 2.0.0 is a rewrite of the version 1.1 released on CRAN in 2015 (archived by CRAN in 2020). The interface changed; see NEWS.md.

Installation

# install.packages("remotes")
remotes::install_github("thiagodoregosousa/GEVStableGarch")

To also build the vignette, install the suggested packages (knitr, rmarkdown, fGarch, …) with dependencies = TRUE. Building it needs pandoc, which comes with RStudio:

remotes::install_github("thiagodoregosousa/GEVStableGarch",
                        dependencies = TRUE, build_vignettes = TRUE)
vignette("GEVStableGarch", package = "GEVStableGarch")

The vignette source can also be read directly in vignettes/GEVStableGarch.Rmd.

Usage

library(GEVStableGarch)

# AR(1)-APARCH(1,1) with stable innovations
spec <- gs_spec(arma = c(1, 0), garch = c(1, 1), aparch = TRUE, dist = gs_stable())

# Simulate from known parameters, then fit
model <- gs_model(spec, mu = 0.0005, ar = 0.05, omega = 0.0002, alpha = 0.05,
                  gamma = 0.3, beta = 0.85, delta = 1.2,
                  dist_par = c(stable_alpha = 1.75, stable_beta = 0))
x <- gs_sim(model, n = 1500, seed = 1)$y
fit <- gs_fit(x, spec)
fit

# Persistence (below 1: stationary scale level)
gs_stationarity(fit)

# One step location, scale and quantiles (VaR is minus the quantile)
predict(fit, n_ahead = 1, level = c(0.01, 0.05))

# Probability integral transform of the residuals (e.g. for copulas)
u <- residuals(fit, type = "pit")

See vignette("GEVStableGarch") for forecasting, rolling windows and user defined distributions.

Functions

Function	Description
`gs_spec()`	Specifies an ARMA(m,n)-GARCH/APARCH(p,q) model and its innovation distribution
`gs_model()`	Attaches parameter values to a specification, with admissibility checks
`gs_fit()`	Maximum likelihood estimation, warm starts, standard errors, stationarity report
`gs_sim()`	Simulates a series from a model
`predict()`	Forecasts location, mean, scale and quantiles; exact one step, simulated beyond
`gs_stationarity()`	Persistence of the APARCH recursion
`gs_aparch_moment()`	$E(\\|z\\| - \gamma z)^\delta$ of the innovations (closed form or numerical)
`gs_stable()`, `gs_gev()`, `gs_gat()`	Built in innovation distributions
`gs_dist()`, `gs_check_dist()`	User defined innovation distributions and their self check
`dgat()`, `pgat()`, `qgat()`, `rgat()`	Density, distribution, quantile and random generation of the GAt distribution

Methods for fitted models: coef(), vcov(), logLik(), AIC(), BIC(), residuals(type = c("raw", "standardized", "pit")), sigma(), fitted(), print().

Package layout

R/: package source (one file per concern: distributions, parameters, filters, likelihood, fit, simulation, forecasting)
tests/testthat/: unit tests, including cross checks against fGarch
vignettes/: worked example
dev/: development material excluded from the build (restructuring plan notes, legacy code of version 1.1, benchmarks, exploratory scripts)
PLAN.md: restructuring plan and decisions

Relationship to other packages

GEVStableGarch builds on existing work and reuses it explicitly:

The ARMA-APARCH filter and model structure follow fGarch (Wuertz, Chalabi and Luksan, 2006); Diethelm Wuertz is credited as contributor and copyright holder in DESCRIPTION.
Maximum likelihood optimization uses Rsolnp (Galanos and Ye, 2025).
The stable density and distribution functions use libstable4u (Royuela-del-Val, Simmross-Wattenberg and Alberola-Lopez, 2017).

The package’s own contribution is the pluggable innovation-distribution interface (gs_dist() / gs_check_dist()) and the closed-form APARCH moments $E(|z| - \gamma z)^\delta$ for the stable, GEV and GAt families, which extend GARCH stationarity and forecasting (the standard fGarch-style recursion) to these heavy-tailed innovations. Estimation, simulation, forecasting and Value-at-Risk are then available for them and for any user-defined distribution.

Reference

Galanos, A., Ye, Y. (2025). Rsolnp: General Non-Linear Optimization. R package version 2.0.1. https://CRAN.R-project.org/package=Rsolnp

Mittnik, S., Paolella, M. S., Rachev, S. T. (2002). Stationarity of stable power-GARCH processes. Journal of Econometrics, 106, 97-107.

Paolella, M. S. (1997). Tail estimation and conditional modeling of heteroskedastic time series. PhD thesis, University of Kiel.

Royuela-del-Val, J., Simmross-Wattenberg, F., Alberola-Lopez, C. (2017). libstable: Fast, Parallel, and High-Precision Computation of alpha-Stable Distributions in R, C/C++, and MATLAB. Journal of Statistical Software, 78(1), 1-25.

Wuertz, D., Chalabi, Y., Luksan, L. (2006). Parameter Estimation of ARMA Models with GARCH/APARCH Errors: An R and SPlus Software Implementation. Journal of Statistical Software.

Zhao, X., Scarrott, C.J., Oxley, L., Reale, M. (2011). GARCH dependence in extreme value models with Bayesian inference. Mathematics and Computers in Simulation, 81(7), 1430-1440.