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WP46: pilot (SPY, AAPL, CL, EURUSD) on the validation period, feasibility report, tail-risk module, multivariate models, empirical tail quantiles in fits; protocol frozen

Simon-Pierre Boucher committed · Nov 9, 2026 parent 7b39a17
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added docs/feasibility_report.md +42 −0
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1+# Feasibility report and Phase 2 pilot (2026-11-09)
2+
3+## Data (after audit and panel construction)
4+- 42 instruments ingested from FinData OS (1-minute bars 2000/2008/2010/2013 → 2026-10-30; 230 M bars in the node cache),
5+ daily panels built with session windows D-02, realized measures D-03, validity rules D-05/D-06.
6+- Proxy sanity: mean(RV5ss + r_on²)/mean(r²) over valid days lies in [0.93, 1.17] for all ETFs, stocks, futures and FX
7+ (bond ETFs/ZN ≈ 1.16–1.24: the overnight share is small and intraday noise slightly inflates RV); crypto only from 2022
8+ (BTC 1.24 on valid days — still noisier, disclosed).
9+- Validity rates: equities 0.75–1.00 (early-year thin trading in IEF, LQD, XLF, XLE, EEM, EFA), futures 0.89–1.00,
10+ FX ≈ 1.00, crypto 0.36 (BTC) / 0.48 (ETH) because of the 2022 cutoff.
11+
12+## Software verification
13+- 19 unit/integration tests, 5 Monte Carlo recovery tests (GJR, NAGARCH, Realized GARCH, HEAVY, MS-GARCH) and the
14+ rugarch 1.5-6 cross-check all pass; custom GARCH(1,1) reproduces arch's recursion to 1e-9 and arch's forecasts to 1e-15;
15+ all arch/custom log-likelihoods are within 0.3 of rugarch's maximum (FIGARCH: arch 1.47 below rugarch, documented).
16+- Leakage: a whole-job test perturbs post-origin returns and realized measures (×3 / ×9) and finds every forecast unchanged
17+ (GJR-t Tier A, HEAVY Tier B; and in the pilot GJR-t + HAR on real panels).
18+
19+## Pilot (validation period 2012-01-03 → 2015-12-31, window 1,000, refit 5 days; `results/metrics/pilot/`)
20+| instrument | origins | models | failures | fit time (s, mean) | notes |
21+|---|---|---|---|---|---|
22+| SPY | 1,006 | 9 | 0 forecast failures; GARCH-t 26/202 inadmissible refits (α+β ≥ 1) | 0.004–0.035 | QLIKE ratio to GARCH-N at h=1: GJR-t 0.88, APARCH-t 0.88, NAGARCH-t 0.89, EGARCH-t 0.93, HAR 0.99, Realized GARCH 0.85 |
23+| AAPL | 1,006 | 9 | 0 | 0.004–0.035 | GJR-t 0.92, EGARCH-t 0.94, APARCH-t 0.94, HAR 1.10, RealGARCH 1.00 |
24+| CL | 1,032 | 9 | 0 | 0.004–0.033 | HAR 0.73, GJR-t 0.94, EGARCH-t 0.96; at h=22 EGARCH-t 0.68 |
25+| EURUSD | 556 | 9 | EGARCH-t 20/556 forecast failures (simulation with inadmissible |β| ≥ 1 fits), GJR-t 23 inadmissible refits | 0.005–0.044 | HAR 0.89, GJR-t 0.92, NAGARCH-t 0.95; EGARCH-t 1.32 (failures excluded → operational penalty) |
26+Exploratory reading only (validation period): asymmetric models and realized-measure models beat GARCH(1,1) at h = 1 on
27+these four instruments; historical 22-day variance is 28–42 % worse; the levels-HAR direct projection is unstable for AAPL
28+(window includes high-variance episodes → large intercept), a known weakness that log-HAR addresses.
29+
30+## Compute budget (measured)
31+Per spec and instrument over 4 years: 0.5–10 s wall (MS-GARCH ≈ 0.08 s/refit, FIGARCH ≈ 0.26 s/refit, APARCH/EGARCH
32+simulation forecasts ≈ 2–3 ms/origin). Main run (3,276 jobs, OOS 2012–2026 ≈ 3,700 origins): ≈ 25–40 CPU-hours →
33+< 1 hour on the six nodes (116 workers). Robustness variants (expanding, window 2,000, refit 22) are affordable.
34+
35+## Risks and mitigations
36+- Inadmissible/near-integrated fits for t-distributed GARCH on FX and index ETFs: kept and flagged; failure-adjusted
37+ results reported; EGARCH simulation failures counted as failures (never replaced).
38+- Thin early-year intraday data for bond/sector ETFs: realized measures invalid on those days; common-sample analysis.
39+- Crypto: realized-measure evaluation only 2022–2026; Tier A daily returns from 2017 (BTC) / 2020 (ETH) with r² proxy as a diagnostic only.
40+- Vendor futures roll rule undocumented: ratio-adjusted continuous series guarantees no roll jumps in returns; RV on roll days spans two contracts (disclosed).
41+
42+Gate 2: **PASS**. Protocol frozen next (tag `prereg-frozen`), then the main run.
added progress.md +36 −0
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1+# WP46 progress log
2+
3+All times ET. "Done" means executed with the listed command and artefact; "planned" means not yet executed.
4+
5+## Phase 0 — Inventory and literature (done 2026-11-09)
6+- Repository reconnaissance: `Recherche-UQO/` conventions (HARMONISATION.md), WP41 as the FinData template; folder
7+ `finance/wp46_garch_benchmark`, repo `gitsrv:srv/git/wp46_uqo.git` created 2026-11-09.
8+- FinData audit: `.venv/bin/python scripts/audit_findata.py` → `docs/findata_audit.md`, `results/manifests/findata_audit.json`
9+ (live API, 42 candidates, 0 errors). Dedicated API key `wp46_uqo_c` (scopes read:market, query, export; two earlier keys revoked).
10+- Literature: `scripts/build_references.py` → `paper/references.bib` (205 entries: 200 Crossref/arXiv/OpenAlex-verified + 5 manual URL),
11+ `docs/literature_matrix.md`, `results/metrics/references_verification.json` (1 unverified: Chung 1999, excluded).
12+- Gate 0: PASS (evidence-backed instrument list; no invented endpoints).
13+
14+## Phase 1 — Pre-registered protocol (done 2026-11-09, freeze tag `prereg-frozen`)
15+- `docs/preregistered_protocol.md`, `configs/{model_registry,forecast_protocol,study,instruments}.yaml`, `docs/methodology_decisions.md` (D-01…D-15).
16+- Disclosure: SPY 2024 forecast values (no losses) were inspected during driver smoke tests before the freeze (D-15);
17+ the pilot (Phase 2) used the validation period 2012–2015 only.
18+
19+## Phase 2 — Trusted data and pilot (done 2026-11-09)
20+- Ingestion on M3U96a: `scripts/ingest_bars.py --workers 3` (1-min + daily bars, 42 instruments + VIX/SPX; manifest
21+ `results/manifests/ingest_manifest.json` with dataset versions and SHA-256) — cache `M3U96a:~/wp46-cache/bars` (not in git).
22+- Panels: `scripts/build_panels.py` (3 runs: tz fix, per-instrument session length D-05, crypto cutoff D-06) →
23+ `~/wp46-cache/panels/*.parquet` on M3U96a, laptop and the 5 other compute nodes; `results/manifests/panels_manifest.json`.
24+- Tests: `pytest tests/unit tests/integration` (19 passed), `pytest tests/simulation -m slow` (5 passed after fixing the
25+ NAGARCH parameter index in the test), `pytest tests/replication -m r` (rugarch 1.5-6 cross-check PASS; `results/metrics/rugarch_crosscheck.json`).
26+- Pilot: `scripts/run_pilot.py --symbols SPY,AAPL` and `--symbols CL,EURUSD` (validation period) → `results/metrics/pilot/`;
27+ leakage check passed (future returns perturbed → forecasts unchanged).
28+- Gate 2: PASS (see `docs/feasibility_report.md`).
29+
30+## Phase 3–5 — Benchmark, realized/multivariate tiers, inference (in progress)
31+- Job list: `scripts/make_jobs.py --name main` → 3,276 jobs (42 instruments × 29 implemented models × distributions), OOS 2012-01-03 → 2026-10-30.
32+- Dispatch: `scripts/dispatch_nodes.py launch --jobs results/manifests/jobs_main.json --name main` (M3U96a/M3U96b/M2U64/M5M36/M4M64a/M4M64c).
33+
34+## Open issues
35+- FIGARCH: arch and rugarch differ by 1.47 log-likelihood units on the fixture (truncation/constraints) — caveat in the model card.
36+- Crypto realized measures unusable before 2022 (D-06): crypto Tier B / proxy-based evaluation covers 2022–2026 only.
modified results/metrics/pilot/pilot_report.json +277 −752
@@ -1,42 +1,31 @@
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@@ -44,169 +33,169 @@
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926− "realgarch11__normal__w1000_r5": 0.0233 451+ "realgarch11__normal__w1000_r5": 0.0267
927 }, 452 },
928 "max": { 453 "max": {
929− "aparch11__t__w1000_r5": 0.105, 454+ "aparch11__t__w1000_r5": 0.0465,
930− "egarch11__t__w1000_r5": 0.0094, 455+ "egarch11__t__w1000_r5": 0.0173,
931− "garch11__normal__w1000_r5": 0.0053, 456+ "garch11__normal__w1000_r5": 0.0063,
932− "garch11__t__w1000_r5": 0.0123, 457+ "garch11__t__w1000_r5": 0.0095,
933− "gjr11__t__w1000_r5": 0.0093, 458+ "gjr11__t__w1000_r5": 0.0127,
934 "har_rv__empirical__w1000_r5": 0.0011, 459 "har_rv__empirical__w1000_r5": 0.0011,
935 "histvar22__empirical__w1000_r5": 0.0, 460 "histvar22__empirical__w1000_r5": 0.0,
936− "nagarch11__t__w1000_r5": 0.0104, 461+ "nagarch11__t__w1000_r5": 0.1042,
937− "realgarch11__normal__w1000_r5": 0.0296 462+ "realgarch11__normal__w1000_r5": 0.0368
938 } 463 }
939 } 464 }
940 } 465 }
modified scripts/run_pilot.py +9 −5
@@ -50,11 +50,15 @@ def main() -> None:
50 tab = Lc.groupby(["proxy", "loss", "h", "spec_id"])["value"].mean().unstack("spec_id") 50 tab = Lc.groupby(["proxy", "loss", "h", "spec_id"])["value"].mean().unstack("spec_id")
51 bench = [s for s in specs if s.startswith("garch11__normal")][0] 51 bench = [s for s in specs if s.startswith("garch11__normal")][0]
52 ratio = tab.div(tab[bench], axis=0) 52 ratio = tab.div(tab[bench], axis=0)
53− # leakage check: perturb returns after the last origin -> forecasts at the last origin unchanged 53+ # leakage check: perturb returns AND realized measures after the last origin -> every forecast of the whole
54− p2 = panel.copy(); last = F["origin"].max(); m = p2["session"] > last; p2.loc[m, "r"] *= 3.0 54+ # job (same refit schedule) is unchanged
55− F2, _ = run_job(p2, JobSpec(sym, "gjr11", "t", "A", oos_start=str(last.date()), oos_end=str(last.date()))) 55+ p2 = panel.copy(); last = F["origin"].max(); m = p2["session"] > last
56− f1 = F[(F.spec_id.str.startswith("gjr11__t")) & (F.origin == last)]["h1"].values 56+ p2.loc[m, "r"] *= 3.0; p2.loc[m, "rv_5m_ss"] *= 9.0
57− leak_ok = bool(np.allclose(f1, F2["h1"].values)) 57+ leak_ok = True
58+ for mid, dist, tier in [("gjr11", "t", "A"), ("har_rv", "empirical", "B")]:
59+ F1 = F[F.spec_id.str.startswith(f"{mid}__{dist}")].sort_values("origin")
60+ F2, _ = run_job(p2, JobSpec(sym, mid, dist, tier, oos_start=a.start, oos_end=a.end))
61+ leak_ok &= bool(np.allclose(F1["h1"].values, F2.sort_values("origin")["h1"].values, equal_nan=True))
58 dm = {s: dm_test(Lc[(Lc.spec_id == s) & (Lc.h == 1) & (Lc.proxy == "rv5ss_on") & (Lc.loss == "qlike")].sort_values("origin")["value"].values, 62 dm = {s: dm_test(Lc[(Lc.spec_id == s) & (Lc.h == 1) & (Lc.proxy == "rv5ss_on") & (Lc.loss == "qlike")].sort_values("origin")["value"].values,
59 Lc[(Lc.spec_id == bench) & (Lc.h == 1) & (Lc.proxy == "rv5ss_on") & (Lc.loss == "qlike")].sort_values("origin")["value"].values, 1) 63 Lc[(Lc.spec_id == bench) & (Lc.h == 1) & (Lc.proxy == "rv5ss_on") & (Lc.loss == "qlike")].sort_values("origin")["value"].values, 1)
60 for s in specs if s != bench} 64 for s in specs if s != bench}
added src/wp46/diagnostics/__init__.py +1 −0
@@ -0,0 +1 @@
1+from .tailrisk import var_es_forecasts, kupiec, christoffersen_cc, engle_manganelli_dq, fz0_loss, backtest_table # noqa: F401
added src/wp46/diagnostics/tailrisk.py +108 −0
@@ -0,0 +1,108 @@
1+"""One-day-ahead VaR / ES forecasts and backtests (percent returns).
2+
3+VaR_p(t+1) = mu_{t+1} + sqrt(h_{t+1}) q_p ; ES_p(t+1) = mu_{t+1} + sqrt(h_{t+1}) e_p, where q_p / e_p are the p-quantile
4+and lower-tail mean of the model's standardized innovation law (normal, t, ged, skewt via wp46.models.distributions). For
5+distribution-free models ('empirical'), q_p and e_p are the empirical quantile / tail mean of the standardized in-window
6+residuals z = (r - mu)/sqrt(sigma2_filtered) supplied by the caller (the driver stores them per refit as `emp_q`).
7+Backtests: Kupiec (1995) unconditional coverage LR, Christoffersen (1998) conditional coverage LR, Engle & Manganelli
8+(2004) dynamic quantile test with 4 lagged hits and the VaR as regressors, Fissler & Ziegel (2016) FZ0 joint loss
9+(Patton, Ziegel & Chen 2019 parameterization): FZ0 = -1/(alpha ES) 1{r<=VaR} (VaR - r) + VaR/ES + log(-ES) - 1, valid for ES < 0."""
10+from __future__ import annotations
11+
12+import numpy as np
13+import pandas as pd
14+from scipy import stats
15+
16+from wp46.models.distributions import expected_shortfall, ppf
17+
18+LEVELS = (0.01, 0.05)
19+
20+
21+def var_es_forecasts(mu: np.ndarray, h1: np.ndarray, dist: str, dp1: np.ndarray, dp2: np.ndarray, levels=LEVELS,
22+ emp_q: dict | None = None) -> dict:
23+ """Vectorized over origins; distribution parameters may vary by origin (refits)."""
24+ out = {}
25+ s = np.sqrt(np.maximum(h1, 1e-12))
26+ for p in levels:
27+ q = np.full(len(mu), np.nan); e = np.full(len(mu), np.nan)
28+ if dist == "empirical":
29+ if emp_q is not None:
30+ q[:] = emp_q[p]["q"]; e[:] = emp_q[p]["es"]
31+ elif dist == "normal":
32+ q[:] = stats.norm.ppf(p); e[:] = -stats.norm.pdf(stats.norm.ppf(p)) / p
33+ else:
34+ params = np.column_stack([dp1, dp2]) if dist == "skewt" else dp1[:, None]
35+ uniq, inv = np.unique(np.round(params, 10), axis=0, return_inverse=True)
36+ for k, prm in enumerate(uniq):
37+ m = inv.ravel() == k
38+ q[m] = ppf(dist, p, prm)[0]
39+ e[m] = expected_shortfall(dist, p, prm)
40+ out[p] = {"var": mu + s * q, "es": mu + s * e}
41+ return out
42+
43+
44+def kupiec(hits: np.ndarray, p: float) -> dict:
45+ n = len(hits); x = int(hits.sum())
46+ if n == 0:
47+ return dict(lr=np.nan, p=np.nan, n=0, x=0, rate=np.nan)
48+ pi = x / n
49+ with np.errstate(divide="ignore", invalid="ignore"):
50+ l0 = x * np.log(p) + (n - x) * np.log(1 - p)
51+ l1 = (x * np.log(pi) if x > 0 else 0.0) + ((n - x) * np.log(1 - pi) if x < n else 0.0)
52+ lr = -2 * (l0 - l1)
53+ return dict(lr=float(lr), p=float(stats.chi2.sf(lr, 1)), n=n, x=x, rate=pi)
54+
55+
56+def christoffersen_cc(hits: np.ndarray, p: float) -> dict:
57+ h = hits.astype(int)
58+ if len(h) < 2:
59+ return dict(lr_ind=np.nan, p_ind=np.nan, lr_cc=np.nan, p_cc=np.nan)
60+ n00 = np.sum((h[:-1] == 0) & (h[1:] == 0)); n01 = np.sum((h[:-1] == 0) & (h[1:] == 1))
61+ n10 = np.sum((h[:-1] == 1) & (h[1:] == 0)); n11 = np.sum((h[:-1] == 1) & (h[1:] == 1))
62+ p01 = n01 / max(n00 + n01, 1); p11 = n11 / max(n10 + n11, 1); pi = (n01 + n11) / max(len(h) - 1, 1)
63+
64+ def ll(a, b, c, d, q0, q1):
65+ with np.errstate(divide="ignore", invalid="ignore"):
66+ t = 0.0
67+ for cnt, pr in ((a, 1 - q0), (b, q0), (c, 1 - q1), (d, q1)):
68+ if cnt > 0:
69+ t += cnt * np.log(pr)
70+ return t
71+ l_ind = ll(n00, n01, n10, n11, p01, p11); l_0 = ll(n00, n01, n10, n11, pi, pi)
72+ lr_ind = -2 * (l_0 - l_ind)
73+ lr_uc = kupiec(hits, p)["lr"]
74+ lr_cc = lr_uc + lr_ind
75+ return dict(lr_ind=float(lr_ind), p_ind=float(stats.chi2.sf(lr_ind, 1)), lr_cc=float(lr_cc), p_cc=float(stats.chi2.sf(lr_cc, 2)))
76+
77+
78+def engle_manganelli_dq(hits: np.ndarray, var: np.ndarray, p: float, lags: int = 4) -> dict:
79+ h = hits.astype(float) - p
80+ n = len(h)
81+ if n <= lags + 10:
82+ return dict(stat=np.nan, p=np.nan)
83+ X = np.column_stack([np.ones(n - lags)] + [h[lags - j - 1:n - j - 1] for j in range(lags)] + [var[lags:]])
84+ y = h[lags:]
85+ XtX = X.T @ X
86+ try:
87+ b = np.linalg.solve(XtX, X.T @ y)
88+ except np.linalg.LinAlgError:
89+ return dict(stat=np.nan, p=np.nan)
90+ stat = float(b @ XtX @ b / (p * (1 - p)))
91+ return dict(stat=stat, p=float(stats.chi2.sf(stat, X.shape[1])))
92+
93+
94+def fz0_loss(r: np.ndarray, var: np.ndarray, es: np.ndarray, p: float) -> np.ndarray:
95+ es = np.minimum(es, -1e-8)
96+ hit = (r <= var).astype(float)
97+ return -hit * (var - r) / (p * es) + var / es + np.log(-es) - 1.0
98+
99+
100+def backtest_table(r: np.ndarray, fc: dict, p: float) -> dict:
101+ var, es = fc[p]["var"], fc[p]["es"]
102+ m = np.isfinite(r) & np.isfinite(var) & np.isfinite(es)
103+ r, var, es = r[m], var[m], es[m]
104+ hits = (r <= var)
105+ k = kupiec(hits, p); c = christoffersen_cc(hits, p); d = engle_manganelli_dq(hits, var, p)
106+ fz = fz0_loss(r, var, es, p)
107+ return dict(n=int(len(r)), hit_rate=k["rate"], kupiec_p=k["p"], cc_p=c["p_cc"], dq_p=d["p"], fz0_mean=float(np.mean(fz)),
108+ es_shortfall_ratio=float(np.mean(r[hits]) / np.mean(es[hits])) if hits.sum() > 0 else np.nan)
modified src/wp46/estimation/rolling.py +22 −1
@@ -66,6 +66,25 @@ def make_model(model_id: str):
66 raise KeyError(model_id) 66 raise KeyError(model_id)
67 67
68 68
69+def _empirical_tail(model, fit, r: np.ndarray, x) -> dict:
70+ """Empirical 1 % / 5 % quantiles and tail means of the standardized in-window residuals z = (r - mu)/sqrt(sigma2)
71+ (used for the VaR/ES of distribution-free models and as a diagnostic for parametric ones)."""
72+ try:
73+ s2 = np.asarray(model.filter(fit, r, x), float)
74+ mu = float(fit.params[0]) if len(fit.params) else float(np.mean(r))
75+ z = (np.asarray(r, float) - mu) / np.sqrt(np.maximum(s2, 1e-12))
76+ z = z[np.isfinite(z)]
77+ out = {}
78+ for p in (0.01, 0.05):
79+ q = float(np.quantile(z, p))
80+ out[f"emp_q{int(p*100):02d}"] = q
81+ out[f"emp_es{int(p*100):02d}"] = float(np.mean(z[z <= q])) if np.any(z <= q) else q
82+ out["z_kurtosis"] = float(np.mean(z ** 4) / np.mean(z ** 2) ** 2)
83+ return out
84+ except Exception: # noqa: BLE001
85+ return {}
86+
87+
69 def run_job(panel: pd.DataFrame, job: JobSpec, progress: bool = False) -> tuple[pd.DataFrame, pd.DataFrame]: 88 def run_job(panel: pd.DataFrame, job: JobSpec, progress: bool = False) -> tuple[pd.DataFrame, pd.DataFrame]:
70 model = make_model(job.model_id) 89 model = make_model(job.model_id)
71 needs_rm = bool(getattr(model, "needs_rm", False)) 90 needs_rm = bool(getattr(model, "needs_rm", False))
@@ -104,13 +123,15 @@ def run_job(panel: pd.DataFrame, job: JobSpec, progress: bool = False) -> tuple[
104 except Exception as e: # noqa: BLE001 123 except Exception as e: # noqa: BLE001
105 new_fit, err = None, f"{type(e).__name__}: {str(e)[:120]}" 124 new_fit, err = None, f"{type(e).__name__}: {str(e)[:120]}"
106 dt = time.perf_counter() - t0 125 dt = time.perf_counter() - t0
126+ emp = {}
107 if new_fit is not None and new_fit.converged: 127 if new_fit is not None and new_fit.converged:
108 fit, stale = new_fit, False 128 fit, stale = new_fit, False
109 status = "ok" if new_fit.admissible else "inadmissible" 129 status = "ok" if new_fit.admissible else "inadmissible"
130+ emp = _empirical_tail(model, new_fit, r, x)
110 else: 131 else:
111 status = "failed" 132 status = "failed"
112 stale = fit is not None 133 stale = fit is not None
113− fits_rows.append(dict(fit_id=fit_id, origin=dates[t], status=status, error=err or (new_fit.notes if new_fit else ""), 134+ fits_rows.append(dict(fit_id=fit_id, origin=dates[t], status=status, error=err or (new_fit.notes if new_fit else ""), **emp,
114 loglik=new_fit.loglik if new_fit else np.nan, n_iter=new_fit.n_iter if new_fit else 0, 135 loglik=new_fit.loglik if new_fit else np.nan, n_iter=new_fit.n_iter if new_fit else 0,
115 n_restarts=new_fit.n_restarts if new_fit else 0, time_s=dt, n_obs=len(r), 136 n_restarts=new_fit.n_restarts if new_fit else 0, time_s=dt, n_obs=len(r),
116 admissible=bool(new_fit.admissible) if new_fit else False, 137 admissible=bool(new_fit.admissible) if new_fit else False,
added src/wp46/models/multivariate.py +154 −0
@@ -0,0 +1,154 @@
1+"""Tier C — covariance forecasts for a fixed basket of N daily return series (percent), h = 1.
2+
3+Models (model_id): rolling_cov252 (sample covariance of the last 252 days), ewma_cov094 (RiskMetrics, lambda 0.94),
4+ccc_garch11 (Bollerslev 1990: univariate GARCH(1,1)-normal per asset + constant correlation of standardized residuals),
5+dcc11 (Engle 2002, two-step QMLE: GARCH(1,1) per asset, then DCC(1,1) correlation targeting with the sample correlation
6+of the standardized residuals; Q_t = (1-a-b) S + a z_{t-1} z_{t-1}' + b Q_{t-1}, R_t = diag(Q_t)^{-1/2} Q_t diag(Q_t)^{-1/2}),
7+adcc11 (Cappiello, Engle & Sheppard 2006: + g n_{t-1} n_{t-1}' with n = z 1{z<0}, targeting (1-a-b) S - g N with
8+N = E[n n']), scalar_bekk11 (Engle & Kroner 1995, scalar: H_t = C C' + a eps_{t-1} eps_{t-1}' + b H_{t-1} with covariance
9+targeting C C' = (1-a-b) Sigma_bar, Gaussian QMLE). All one-step forecasts are symmetric positive definite by construction
10+(checked: minimum eigenvalue > 0 is recorded). Parameters are estimated by Gaussian QMLE with scipy; standardized
11+residuals of the first step come from wp46.models.arch_models GARCH(1,1).
12+"""
13+from __future__ import annotations
14+
15+import math
16+import time
17+
18+import numpy as np
19+from scipy import optimize
20+
21+from .arch_models import ArchModel
22+
23+
24+def _corr_from_cov(H):
25+ d = 1.0 / np.sqrt(np.diag(H))
26+ return H * np.outer(d, d)
27+
28+
29+def _univariate_garch(R: np.ndarray):
30+ """Fit GARCH(1,1)-normal to each column; return (sigma2 matrix T x N, one-step variance forecasts, fits)."""
31+ T, N = R.shape
32+ S2 = np.empty((T, N)); f1 = np.empty(N); fits = []
33+ m = ArchModel("garch11")
34+ for j in range(N):
35+ f = m.fit(R[:, j], dist="normal")
36+ S2[:, j] = m.filter(f, R[:, j])
37+ f1[j] = m.forecast(f, R[:, j], None, 1).step_var[0]
38+ fits.append(f)
39+ return S2, f1, fits
40+
41+
42+def _dcc_negll(theta, Z, S, asym, Nbar):
43+ a = 1 / (1 + math.exp(-theta[0])); b = (1 - a) / (1 + math.exp(-theta[1])); g = 0.0
44+ if asym:
45+ g = (1 - a - b) / (1 + math.exp(-theta[2])) * 0.999
46+ T, N = Z.shape
47+ Q = S.copy(); ll = 0.0
48+ Qbar = (1 - a - b) * S - (g * Nbar if asym else 0.0)
49+ try:
50+ for t in range(T):
51+ if t > 0:
52+ z = Z[t - 1]
53+ Q = Qbar + a * np.outer(z, z) + b * Q
54+ if asym:
55+ n = z * (z < 0)
56+ Q = Q + g * np.outer(n, n)
57+ Rt = _corr_from_cov(Q)
58+ L = np.linalg.cholesky(Rt)
59+ w = np.linalg.solve(L, Z[t])
60+ ll += -0.5 * (2 * np.sum(np.log(np.diag(L))) + w @ w - Z[t] @ Z[t])
61+ except np.linalg.LinAlgError:
62+ return 1e10
63+ return -ll
64+
65+
66+class CovModel:
67+ def __init__(self, model_id: str):
68+ self.model_id = model_id
69+
70+ def fit_forecast(self, R: np.ndarray) -> dict:
71+ """R: T x N returns (window). Returns dict(H1 = one-step covariance forecast, params, converged, time_s, min_eig)."""
72+ t0 = time.perf_counter()
73+ T, N = R.shape
74+ Rc = R - R.mean(axis=0)
75+ mid = self.model_id
76+ params = {}; conv = True
77+ if mid == "rolling_cov252":
78+ H1 = np.cov(Rc[-252:].T, bias=True)
79+ elif mid == "ewma_cov094":
80+ lam = 0.94; H = np.cov(Rc[:50].T, bias=True)
81+ for t in range(T):
82+ H = lam * H + (1 - lam) * np.outer(Rc[t], Rc[t])
83+ H1 = H
84+ elif mid in ("ccc_garch11", "dcc11", "adcc11"):
85+ S2, f1, fits = _univariate_garch(R)
86+ Z = Rc / np.sqrt(S2)
87+ S = np.corrcoef(Z.T)
88+ D1 = np.sqrt(f1)
89+ if mid == "ccc_garch11":
90+ R1 = S
91+ else:
92+ asym = mid == "adcc11"
93+ Nn = Z * (Z < 0); Nbar = (Nn.T @ Nn) / T
94+ th0 = np.array([math.log(0.02 / 0.98), math.log(0.95 / 0.05)] + ([math.log(0.02 / 0.98)] if asym else []))
95+ res = optimize.minimize(_dcc_negll, th0, args=(Z, S, asym, Nbar), method="L-BFGS-B", options={"maxiter": 500})
96+ conv = bool(res.success) and res.fun < 1e9
97+ a = 1 / (1 + math.exp(-res.x[0])); b = (1 - a) / (1 + math.exp(-res.x[1])); g = (1 - a - b) / (1 + math.exp(-res.x[2])) * 0.999 if asym else 0.0
98+ params = {"a": a, "b": b, "g": g, "loglik": -float(res.fun)}
99+ Q = S.copy(); Qbar = (1 - a - b) * S - g * Nbar
100+ for t in range(1, T + 1):
101+ z = Z[t - 1]
102+ Q = Qbar + a * np.outer(z, z) + b * Q
103+ if asym:
104+ n = z * (z < 0); Q = Q + g * np.outer(n, n)
105+ R1 = _corr_from_cov(Q)
106+ H1 = R1 * np.outer(D1, D1)
107+ params.update({f"garch_{j}": list(map(float, f.params)) for j, f in enumerate(fits)})
108+ elif mid == "scalar_bekk11":
109+ Sig = np.cov(Rc.T, bias=True)
110+
111+ def negll(th):
112+ a = 1 / (1 + math.exp(-th[0])); b = (1 - a) / (1 + math.exp(-th[1]))
113+ C = (1 - a - b) * Sig; H = Sig.copy(); ll = 0.0
114+ try:
115+ for t in range(T):
116+ if t > 0:
117+ H = C + a * np.outer(Rc[t - 1], Rc[t - 1]) + b * H
118+ L = np.linalg.cholesky(H); w = np.linalg.solve(L, Rc[t])
119+ ll += -0.5 * (2 * np.sum(np.log(np.diag(L))) + w @ w)
120+ except np.linalg.LinAlgError:
121+ return 1e10
122+ return -ll
123+ res = optimize.minimize(negll, np.array([math.log(0.05 / 0.95), math.log(0.9 / 0.1)]), method="L-BFGS-B", options={"maxiter": 500})
124+ conv = bool(res.success) and res.fun < 1e9
125+ a = 1 / (1 + math.exp(-res.x[0])); b = (1 - a) / (1 + math.exp(-res.x[1]))
126+ C = (1 - a - b) * Sig; H = Sig.copy()
127+ for t in range(1, T + 1):
128+ H = C + a * np.outer(Rc[t - 1], Rc[t - 1]) + b * H
129+ H1 = H; params = {"a": a, "b": b, "loglik": -float(res.fun)}
130+ else:
131+ raise KeyError(mid)
132+ H1 = 0.5 * (H1 + H1.T)
133+ return {"H1": H1, "params": params, "converged": conv, "time_s": time.perf_counter() - t0,
134+ "min_eig": float(np.linalg.eigvalsh(H1).min())}
135+
136+
137+def frobenius_loss(Y: np.ndarray, H: np.ndarray) -> float:
138+ return float(np.sum((Y - H) ** 2))
139+
140+
141+def mv_qlike(Y: np.ndarray, H: np.ndarray) -> float:
142+ """Multivariate QLIKE (Laurent, Rombouts & Violante 2013): log|H| + tr(H^{-1} Y) - log|Y| - N (>= 0 iff Y, H SPD)."""
143+ N = Y.shape[0]
144+ Hi = np.linalg.inv(H)
145+ sy, ldy = np.linalg.slogdet(Y); sh, ldh = np.linalg.slogdet(H)
146+ if sy <= 0 or sh <= 0:
147+ return float("nan")
148+ return float(ldh + np.trace(Hi @ Y) - ldy - N)
149+
150+
151+def portfolio_variance_loss(Y: np.ndarray, H: np.ndarray, w: np.ndarray) -> float:
152+ """QLIKE of the equally weighted (or given w) portfolio variance."""
153+ y = float(w @ Y @ w); h = float(w @ H @ w)
154+ return y / h - math.log(y / h) - 1.0
modified tests/integration/test_rolling_driver.py +13 −0
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