Changes in version 2.0.0 (2026-11-03)                  

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).