Composable models and A/B tests of the 2024 ideas; add powerlaw.

Models are now a Composite of drift, volatility and (optional) shape
components, so an experiment can swap one part against a fixed control.

btcmodel/experiments.py holds seven experiments built from the ideas in the
old branches (catalogued in docs/2024-ideas.md), each with its hypothesis
and source, and a verdict rule fixed before anything ran. `just ab` runs
them on development data. Results:

- Shrinking the cycle drift, and a power-law trend (plain or reverting),
  beat their controls. The power law beats the random walk by 53-63% at
  3-4 years with unbiased outcomes, so it is promoted to MODELS.
- Every alternative volatility estimate (EWMA blends, other windows,
  reversion to a level or trend) is worse than the trailing 365-day window.
  Cycle-dependent volatility, heavy tails and stretched cycle phase show no
  reliable effect.

tests/test_components.py

@@ -0,0 +1,66 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from btcmodel.experiments import EXPERIMENTS
+from btcmodel.halving import GENESIS
+from btcmodel.models.drift import CycleDrift, PowerLawDrift, ShrunkDrift
+from btcmodel.models.shape import StudentT
+from btcmodel.models.volatility import ReversionVol, TrailingVol
+
+from .test_models import synthetic_prices
+
+ALL_VARIANTS = {m.name: m for e in EXPERIMENTS.values() for m in e.models}
+
+
+@pytest.mark.parametrize("name", list(ALL_VARIANTS))
+def test_experiment_models_produce_valid_forecasts(name):
+    prices = synthetic_prices(lambda day: 0.001 + 0 * day, noise=0.03)
+    horizons = np.array([1, 30, 365, 1460])
+    f = ALL_VARIANTS[name].forecast(prices, horizons)
+    assert np.isfinite(f.log_quantiles).all()
+    assert np.all(np.diff(f.log_quantiles, axis=1) >= 0)
+    lo, hi = f.interval(0.8)
+    assert np.all(np.diff(hi - lo) > 0)
+
+
+def test_shrunk_drift_scales_linearly():
+    prices = synthetic_prices(lambda day: np.where(day < 700, 0.002, -0.001))
+    horizons = np.array([100, 1000])
+    full = CycleDrift().expected_log_return(prices, horizons)
+    np.testing.assert_allclose(
+        ShrunkDrift(CycleDrift(), 0.5).expected_log_return(prices, horizons), full / 2
+    )
+    np.testing.assert_allclose(
+        ShrunkDrift(CycleDrift(), 0.0).expected_log_return(prices, horizons), 0
+    )
+
+
+def test_power_law_recovers_its_exponent():
+    dates = pd.date_range("2011-01-01", "2024-11-26", freq="D", name="date")
+    t = (dates - GENESIS).days.to_numpy()
+    prices = pd.DataFrame({"close": 1e-17 * t**5.8}, index=dates)
+    _, slope, _ = PowerLawDrift().fit(prices)
+    assert slope == pytest.approx(5.8, rel=1e-6)
+    expected = 5.8 * np.log((t[-1] + 365) / t[-1])
+    assert PowerLawDrift().expected_log_return(prices, np.array([365]))[0] == pytest.approx(
+        expected
+    )
+
+
+def test_reversion_vol_matches_trailing_when_already_at_long_run():
+    rng = np.random.default_rng(0)
+    dates = pd.date_range("2011-01-01", "2024-11-26", freq="D", name="date")
+    prices = pd.DataFrame(
+        {"close": 100 * np.exp(np.cumsum(0.03 * rng.standard_normal(len(dates))))}, index=dates
+    )
+    horizons = np.array([30, 365, 1460])
+    reverting = ReversionVol(now_span=1460, long_window=len(dates)).sd(prices, horizons)
+    flat = TrailingVol(window=len(dates)).sd(prices, horizons)
+    np.testing.assert_allclose(reverting, flat, rtol=0.05)
+
+
+def test_student_t_shape_has_unit_variance_and_fatter_tails():
+    q = StudentT(4).standard_quantiles(None, np.array([1]))[0]
+    assert q[-1] > 2.576  # beyond the normal 99.5% quantile
+    assert np.interp(0.8413, np.linspace(0.005, 0.995, 100), q) < 1.0  # thinner shoulders