GEVStableGarch 2.0.0

Complete rewrite. The version 1.1 interface (gsFit, gsSpec, gsSim, gsSelect, S4 classes) is replaced; the package was archived on CRAN in 2020, so no compatibility layer is provided.

Scope

• Innovations: stable (S0 parametrization only, via libstable4u), GEV and GAt. Normal, t, skew t and GED innovations are left to fGarch and rugarch; S1 and S2 stable parametrizations and the stable package are dropped.
• Any other distribution can be plugged in with gs_dist(), which requires every field the machinery needs (including when moments exist) and checks them against each other (gs_check_dist()).

New interface

• gs_spec(), gs_model(): specification and parameters as plain lists.
• gs_fit(): maximum likelihood on internally rescaled data, sqp (Rsolnp) or nlminb, warm starts through start, optional Hessian, standard errors set to NA with a warning when a parameter is on a bound or the Hessian is not usable, persistence warning. It records convergence diagnostics in $diagnostics (scaled gradient, Hessian reciprocal condition number and definiteness, optimizer iterations) and warns when the gradient is not near zero, the Hessian is ill conditioned, or the iteration cap is hit.
• gs_bootstrap(): parametric bootstrap standard errors and percentile confidence intervals, recommended over the Hessian errors near a boundary and for GEV innovations, whose support depends on the shape parameter.
• gs_sim(), predict(): simulation and forecasting (exact one step, APARCH recursion and simulated paths beyond).
• gs_stationarity(), gs_aparch_moment().
• S3 methods: coef, vcov, logLik, residuals (raw, standardized, pit), sigma, fitted, print.

Behaviour changes

• The mean equation is in intercept form, as in Wuertz et al. (2006) and fGarch: mu is the intercept, the unconditional location is mu / (1 - sum(ar)).
• The recursion starts from mean(|e|^delta), which is scale equivariant. Starting from fGarch’s own initial value, the likelihood reproduces fGarch exactly for GARCH and APARCH models.
• Stationarity is reported after fitting, not imposed (the old sqp.restriction algorithm is not available).
• The APARCH power delta is no longer bounded below by 1 for stable innovations; delta < stable_alpha is enforced instead. Version 1.1 estimates at delta = 1 were on that bound.

Bug fixes

• pgat() kept only a few digits next to zero; it now uses the exact upper beta tail.
• The out-of-bounds penalty is now graded: it adds a term proportional to the size of the constraint violation (for example delta above the innovation moment bound, or a non-stationary AR polynomial) instead of a flat constant. The objective slopes back toward the feasible region, so the optimizer no longer stalls on a flat plateau.

Performance

• The stable density from libstable4u is about 90 times faster than stabledist (2000 points: 31 ms against 2.9 s). A stable AR(1)-APARCH(1,1) fit on 2000 observations takes about 20 seconds with standard errors and 3 seconds from a warm start (dev/bench/bench_stable_density.R).