ENH: Add the NGARCH volatility process

[bashtage]

Target 9.1: merge after v9.0.0 is tagged. Closes #636.

Adds arch.univariate.NGARCH(p=1, o=1, q=1) (o <= p): the nonlinear asymmetric GARCH of
Engle and Ng (1993), which rugarch calls NAGARCH.

sigma2_t = omega + sum_i alpha_i (e_{t-i} - theta_i sigma_{t-i})^2 + sum_j beta_j sigma2_{t-j}

Sign convention: theta > 0 is the leverage effect. It was settled from the NBER working
paper (w3681), whose estimated model reads (e - 0.2683 sqrt(h))^2, and it matches rugarch's
eta21. The class Notes explain the naming clash with Higgins and Bera (1992).

What is included:

• A compiled ngarch_recursion with a numba/Python twin and a .pyi stub.
• NGARCHUpdater, so ARCHInMean works with NGARCH, including pickling.
• arch_model(vol="ngarch"). o defaults to 0 as for every vol, so o=1 gives the
  shift.
• The analytic forecasts are exact at every horizon, f_h = omega + phi f_{h-1} with
  phi = sum alpha (1 + theta^2) + sum beta, for any standardized distribution, because
  E[(z - theta)^2] = 1 + theta^2.
• Simulation and bootstrap forecasts, simulate, and the crash guards.
• Constraint: the linear sum(alpha) + sum(beta) < 1 plus non-negativity, as for APARCH.
  The Notes and the docs example tell users to check the stationarity condition
  sum(alpha (1 + theta^2)) + sum(beta) < 1.

Validation: rugarch 1.5-6 on R 4.6.1, fGARCH/NAGARCH.

• Variances to 4e-15 relative and log-likelihoods to 6e-14, for normal and Student-t,
  with matched initial values. rugarch's fGARCH filter adds an undocumented 1e-6 inside
  (z - eta)^2. That was confirmed on three parameter sets and is accounted for.
• 10-step forecasts to 1e-6.
• Fits on 4,000 observations: estimates within 0.008.
• For an ARCH order of 2, rugarch's fGARCH disagrees with its own sGARCH, so p >= 2 is
  validated against an independent NumPy recursion and simulation instead.

Tests:

• test_ngarch.py (154): the recursion against NumPy for 7 orders; Cython against numba
  against Python; theta = 0 equals GARCH; the updaters against the recursion.
• Analytic forecasts against simulated means within 4 standard errors (normal and
  skew-t), and parameter recovery for (1,1,1), (2,1,1) and (2,2,1).
• arch_model, fix and ARCHInMean integration.
• NGARCH is added to the existing validation, crash-guard, updater, string-option and
  integer-input lists.
• Each of 6 deliberately introduced bugs is caught.
• Fast suite 27,459 passed. The tests pass in random orders, and the numba path passes on
  Python 3.10. numpydoc lint 0, and the docs build has no new warnings.

For review:

• Should arch_model(vol="ngarch") default o to 1?
• Use the exact nonlinear constraint only if users report persistence of 1 or more.

Thanks to @itsNH98 for the request.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 99.61941% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.97%. Comparing base (d2c90b4) to head (5aa657d).
⚠️ Report is 6 commits behind head on main.

Files with missing lines	Patch %	Lines
arch/univariate/volatility.py	97.76%	2 Missing and 2 partials ⚠️

Additional details and impacted files

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- Misses        256      258       +2     
- Partials       58       60       +2     

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