Fix/inference dof serialization

[ArdiaD]

Five bugs in the reporting and persistence layer around the likelihood, plus regression
tests for each. The likelihood itself is not touched: no estimate, log-likelihood,
conditional variance or state probability changes anywhere in this branch. What changes is
what summary() prints, what AIC/BIC count, what predict() returns for a Bayesian
fit, and whether a saved fit can be reloaded at all.

Everything below is reproduced on data("SMI") with the shipped code. R CMD check --as-cran is unchanged by the branch (2 WARNINGs, 1 NOTE, testthat OK — and the version
bump in the last commit clears one of the two WARNINGs).

1. Standard errors used the delta method transposed — R/Inference.R:38

mSandwitch <- t(mJacob) %*% mInvHessian %*% mJacob   # -> mJacob %*% mInvHessian %*% t(mJacob)

numDeriv::jacobian returns ∂f_i/∂x_j, so Var(g(θ̂)) = J V J'. The two orientations
agree only if J is symmetric, and it is not: the working→natural map is triangular inside
each regime (the sGARCH bound on beta is 0.9999 − alpha1; the gjrGARCH and tGARCH bounds
on beta also involve alpha2 and the shape/skew parameters), and the transition-probability
block is anti-diagonal.

On the default MS(2)-GARCH(1,1)-Normal fit to SMI, checked against the observed information
computed directly in the natural parameterisation:

	natural-scale H	fixed (J V J')	before (J' V J)
alpha1_1	0.01606	0.01511	0.03413
beta_1	0.02197	0.02091	0.00958
alpha1_2	0.00431	0.00437	0.00610
beta_2	0.00416	0.00426	0.00049
P_1_1	0.00982	0.00973	0.00059
P_2_1	(at bound)	0.03072	0.50250

Six of eight were wrong, by factors from 0.06× to 16×. Because the P block is anti-diagonal,
transposing exchanged the two transition probabilities' standard errors. Only alpha0_k,
whose map is a plain exp, was unaffected.

2. Pr(>|t|) was one-sided — R/Inference.R:43

1 - pnorm(abs(t)) under a two-sided label; now 2 * (1 - pnorm(abs(t))).

3. AIC/BIC mis-counted regime.const.pars — R/Utils.R:420

A regime-constant parameter leaves one free value where there were K, so it removes K − 1
degrees of freedom (cf. f_rename_par, which strips name_2 … name_K). dofMSGARCH
subtracted one, which is right only at K = 2: with a regime-constant shape parameter the df
was 17 instead of 16 at K = 3 and 27 instead of 25 at K = 4, always over-penalising the
constrained model.

4. Saved specs and fits could not be reloaded — R/Utils.R:349-353

R serializes external pointers as NULL, so a saveRDS-ed spec or fit comes back with dead
pointers. f_check_spec exists to rebuild them, but the rebuild branch called
spec$rcpp.func$get_mean() / get_sd() — the very pointer whose failure had just triggered
the branch:

Volatility(fit) : Error in .External(...): NULL value passed as symbol address
State(fit)      : Error in .External(...): NULL value passed as symbol address
predict(fit)    : Error in .External(...): NULL value passed as symbol address

The two values read there are already held on the R side in spec$prior.mean /
spec$prior.sd, which the next two lines were using anyway, so the C++ round trip was dead
code. Removing it makes the rebuild work; a reloaded spec, ML fit or MCMC fit now returns
values identical to before it was saved, with user priors preserved.

This is the ordinary workflow of fitting a model, saving it, and analysing it in a later
session — or shipping a spec to a parLapply worker.

5. predict() on an MCMC fit returned draw #1 — R/CondVol.R:32

vol is (T+1) × ndraw and the one-step-ahead value was vol[dim(PredProb)[1]] — a single
index into a matrix is linear indexing, i.e. the last row of the first column. On a
100-draw chain fitted to SMI the reported value was 1.019753 (the first draw) against a
posterior mean of 1.039776, with a spread of 0.999837–1.097337 across draws. Volatility()
already averaged correctly, so the two methods disagreed on the same fit. The
single-parameter (ML) path is unchanged.

Tests

test_Inference.R and test_Serialization.R are new; test_Volatility.R gains one block.
11 blocks, 34 assertions, +13s of check time. All 11 fail on the current code.

Two things worth pointing out, since they are what makes the tests worth having:

• The standard-error test is anchored on a single-regime GARCH(1,1)-Normal, not on the
  MS(2) default. Every parameter there is interior, so a central-difference Hessian of the
  natural-scale negative log-likelihood is well conditioned: it agrees with J V J' to 1e-4
  in relative terms while the transposed sandwich is off by 44% and 85%. That is an
  independent check on the value, not a restatement of the formula.
• Every block opens with a guard asserting its own precondition — the two sandwich
  orientations really differ for this model; the round trip really did invalidate the
  pointers; the posterior mean really differs from the first draw — so none of them can pass
  vacuously if the surrounding code changes.

The K = 3 and K = 4 legs of the degrees-of-freedom test run against a fit-shaped list
rather than a real fit, because a constrained K ≥ 3 model cannot currently be fitted at
all (see below).

Not in this branch

The last commit (version bump + NEWS) is separable — drop it if the release number should
be decided elsewhere; nothing depends on it.

A review of the package turned up nine further issues that are not addressed here,
several of them more serious than some of the above. The two worth flagging now:

• src/MSgarch.h:283 computes the ergodic distribution with a raw Armadillo .i() on
  I − P + U, on every likelihood evaluation. When do.plm = TRUE — forced by fixed.pars
  and regime.const.pars, and hard-coded in FitMCMC — the free transition entries are
  mapped into (0,1) independently, so for K ≥ 3 a row can leave the simplex, the matrix
  can be exactly singular, and the uncaught exception aborts the entire run. Reproducible:
  FitML on a K = 3 spec with regime.const = "nu" dies at
  P = [[1, 0.999973, −0.999973], [0,1,0], [0,0,1]]. This is why the tests above cannot fit
  a constrained K ≥ 3 model.
• R/FitML.R:133 guards optimisation failure with if (llk == 1e+10), but f_nll
  returns +1e10 so llk is −1e10; and f_OptimFUNDefault wraps optim in try(), so
  optimizer$value errors first. Every failure mode — including a single NA in the data,
  which f_check_y lets through — therefore surfaces as
  Error in optimizer$value : $ operator is invalid for atomic vectors.

Happy to open these as separate issues or as a follow-up PR, whichever you prefer.