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.
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.gs_dist(), which requires
every field the machinery needs (including when moments exist) and checks
them against each other (gs_check_dist()).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().coef, vcov, logLik, residuals (raw, standardized, pit),
sigma, fitted, print.mu is the intercept, the unconditional location is
mu / (1 - sum(ar)).mean(|e|^delta), which is scale equivariant.
Starting from fGarch's own initial value, the likelihood reproduces fGarch
exactly for GARCH and APARCH models.sqp.restriction algorithm is not available).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.pgat() kept only a few digits next to zero; it now uses the exact upper
beta tail.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.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).