fix(garch): use a zero point forecast for GARCH and ARCH

[AnthonyOlakangil]

Closes #1280

Problem

GARCH and ARCH return a random draw as the point forecast, and the prediction intervals are built around it. garch_forecast simulates a path (yhat = error * sqrt(sigma2hat) with error ~ N(0, 1)) and returns that path as mean, and GARCH.predict / GARCH.forecast then set lo/hi = mean -/+ z * sqrt(sigma2).

Both models are zero-mean (y_t = eps_t * sigma_t), so the forecast of the conditional mean is 0 at every horizon. Because garch_forecast also calls np.random.seed(1), the first step is always the same draw, about +1.62 * sigma, so the bands are shifted rather than just noisy.

Change

garch_forecast returns np.zeros(h) for mean. sigma2 and fitted are unchanged, so the half-width of the intervals is the same as before and they are now centred on 0.

The sigma2 recursion still uses the simulated path for future squared values. That is what #1264 fixes, and the two changes are independent.

How tested

• Regression tests: test_garch_forecast in tests/test_garch.py now checks that mean is all zeros, and a new TestGARCH::test_garch_intervals_centred_on_zero in tests/test_models.py checks the mean and that the 95% band is symmetric around 0. Both fail on main and pass with this change.
• pytest tests/test_garch.py tests/test_models.py::TestGARCH tests/test_models.py::TestARCH: 18 passed.
• pre-commit run (ruff, mypy) on the changed files passes.

Repro from the issue (y = rng.standard_normal(500) * 10, h=5):

before: GARCH mean: [ 16.5331  -6.2267  -5.3759 -10.921    8.8084]
        ARCH  mean: [ 16.4802  -6.2067  -5.3587 -10.8861   8.7802]
after:  GARCH mean: [0. 0. 0. 0. 0.]
        ARCH  mean: [0. 0. 0. 0. 0.]

One-step-ahead coverage of the 95% interval on 1000 simulated GARCH(1,1) series (w=0.5, alpha=0.1, beta=0.8, length 500, fitted with GARCH(1, 1)):

before: 0.637
after:  0.951

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