v1b_walkforward.md

V1b — Walk-forward calibration backtest

Method. Rolling-origin expanding-window walk-forward. For each cutoff in ['2019-01-01', '2020-01-01', '2021-01-01', '2022-01-01', '2023-01-01', '2024-01-01'], train calibration surface on bounds with fri_ts < cutoff, evaluate Oracle on bounds in [cutoff, cutoff + 12 months). For each τ ∈ {0.68, 0.85, 0.95, 0.99}, sweep buffer over [0.000, 0.060] step 0.005 and pick the smallest passing realized ≥ τ−0.005 + Kupiec $p_{uc}$ > 0.10 + Christoffersen $p_{ind}$ > 0.05.

Per-target buffer summary across splits

target	n_splits	buffer_mean	buffer_std	buffer_min	buffer_max	deployed_buffer	realized_mean	realized_std	p_uc_min	n_pass
0.680	6.000	0.016	0.022	0.000	0.055	0.045	0.706	0.030	0.000	3.000
0.850	6.000	0.025	0.022	0.000	0.055	0.045	0.859	0.017	0.045	4.000
0.950	6.000	0.019	0.017	0.000	0.045	0.020	0.951	0.012	0.004	5.000
0.990	6.000	0.050	0.024	0.000	0.060	0.005	0.970	0.017	0.000	1.000

Per-split detail

split	cutoff	horizon_end	n_train_b	n_test_p	target	buffer_chosen	realized	mean_half_width_bps	p_uc	p_ind	status
0	2019-01-01	2020-01-01	50088	468	0.680	0.010	0.679	75.091	0.981	0.592	PASS
0	2019-01-01	2020-01-01	50088	468	0.850	0.035	0.853	123.024	0.876	0.365	PASS
0	2019-01-01	2020-01-01	50088	468	0.950	0.025	0.947	251.777	0.737	0.383	PASS
0	2019-01-01	2020-01-01	50088	468	0.990	0.060	0.966	314.701	0.000	0.808	CEILING
1	2020-01-01	2021-01-01	61320	477	0.680	0.030	0.709	173.409	0.177	0.054	PASS
1	2020-01-01	2021-01-01	61320	477	0.850	0.055	0.849	299.856	0.954	0.068	PASS
1	2020-01-01	2021-01-01	61320	477	0.950	0.045	0.948	677.093	0.810	0.725	PASS
1	2020-01-01	2021-01-01	61320	477	0.990	0.060	0.948	677.093	0.000	0.725	CEILING
2	2021-01-01	2022-01-01	72768	489	0.680	0.000	0.753	118.042	0.000	0.568	CEILING
2	2021-01-01	2022-01-01	72768	489	0.850	0.000	0.881	193.907	0.045	0.542	CEILING
2	2021-01-01	2022-01-01	72768	489	0.950	0.000	0.947	340.903	0.750	0.842	PASS
2	2021-01-01	2022-01-01	72768	489	0.990	0.060	0.980	569.905	0.042	0.606	CEILING
3	2022-01-01	2023-01-01	84252	520	0.680	0.000	0.731	184.602	0.012	0.860	CEILING
3	2022-01-01	2023-01-01	84252	520	0.850	0.000	0.879	285.878	0.058	0.165	MARGINAL
3	2022-01-01	2023-01-01	84252	520	0.950	0.000	0.975	492.380	0.004	0.012	CEILING
3	2022-01-01	2023-01-01	84252	520	0.990	0.000	0.996	723.292	0.107	0.686	PASS
4	2023-01-01	2024-01-01	96384	520	0.680	0.000	0.679	108.344	0.955	0.375	PASS
4	2023-01-01	2024-01-01	96384	520	0.850	0.020	0.846	194.044	0.807	0.312	PASS
4	2023-01-01	2024-01-01	96384	520	0.950	0.020	0.946	358.609	0.691	0.846	PASS
4	2023-01-01	2024-01-01	96384	520	0.990	0.060	0.973	402.716	0.001	0.746	CEILING
5	2024-01-01	2025-01-01	108864	520	0.680	0.055	0.687	122.973	0.749	0.002	MARGINAL
5	2024-01-01	2025-01-01	108864	520	0.850	0.040	0.846	197.577	0.807	0.163	PASS
5	2024-01-01	2025-01-01	108864	520	0.950	0.025	0.946	398.090	0.691	0.866	PASS
5	2024-01-01	2025-01-01	108864	520	0.990	0.060	0.956	448.519	0.000	0.928	CEILING

Reading

• buffer_mean ± buffer_std is the empirical distribution of optimal buffers across walk-forward splits — the single-split values in BUFFER_BY_TARGET should fall within ~1σ of buffer_mean.
• n_pass / n_splits is the fraction of splits in which the chosen buffer satisfies the strict (PASS) criteria. Lower fractions reveal targets where calibration is fundamentally harder (typically the tails).
• realized_std quantifies how stable the served calibration is across deployment windows; small values support a fixed BUFFER_BY_TARGET schedule with rolling re-fits, large values argue for adaptive per-window re-tuning.

Use

1. For paper §9.4 ('sample-size-one buffer' disclosure): replace with measured buffer_mean ± buffer_std per τ.
2. For deployment cadence (docs/v2.md §V2.2): the realized_std figure caps the rolling rebuild interval — if drift is bounded, quarterly rebuilds suffice; otherwise monthly or event-driven.
3. For grant application (docs/grant_application_tldr.md): the walk-forward result is the Tier-1 deliverable that converts a single-split anchor into a distribution-valued claim.